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A NEW APPROACH IN EMPIRICAL MODELLING

OF CO2 CORROSION WITH THE PRESENCE OF

HAc AND H2S

YULI PANCA ASMARA

DOCTOR OF PHILOSOPHY

MECHANICAL ENGINEERING

UNIVERSITI TEKNOLOGI PETRONAS

NOVEMBER 2010

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Abstract

CO2 corrosion is the main threat in upstream oil and gas operations. The requirement

to predict the corrosion in design and operational stage is critical. However, the

presence of other corrosion species and operational parameters complicate the

mechanism of the corrosion. The interaction between those factors affect the accuracy

of the corrosion prediction. Although many publications on CO2 corrosion prediction

had been published, most of the prediction models rely on specific algorithms to

combine individual effect of the interacting species to represent the total corrosion

rate. This effort is inefficient and needs a large number of experiments to process all

possible corrosion data simultaneously. In order to study CO2 corrosion of carbon

steel involving interactive effects of several key parameters, a proven systematic

statistical method that can represent the multitude interactive effects is needed. In this

research, a combination of response surface methodology (RSM) and mechanistic

corrosion theories were used to construct an empirical model that relates the effects of

acetic acid (HAc), temperature, and rotation speed on CO2 and CO2/H2S corrosion

rate simultaneously. The corrosion experiments are based on both linear polarization

resistance (LPR) and electrochemical impedance spectroscopy (EIS) methods. Flow

condition is simulated using rotating cylinder electrode (RCE). The RSM regression

models for the carbon steel corrosion in CO2 environments involving HAc,

temperature and rotation speed as parameters have been successful developed and

validated with experimental data and commercial predictive models. In the form of

mathematical equations, the effects of independent variables will be easily identified

and developed. The combination RSM and mechanistic theory applied in this research

is efficient to determine the empirical relationship of the variables tested

simultaneously. Furthermore, RSM models can be used to determine scaling

temperature, limiting current density and flow dependency characters.

Key words: CO2 corrosion, response surface methodology, corrosion model.

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Abstrak

Kakisan karbon dioxide (CO2) adalah merupakan masalah utama kepada operasi

huluan bagi industri minyak dan gas bumi. Keperluan untuk meramal tahapan kakisan

di dalam peringkat reka bentuk dan operasi adalah kritikal. Kehadiran spesies-spesies

kakisan yang lain dan juga parameter operasi menjadikan mekanisme kakisan

bertambah kompleks antara fakor-faktor berkenaan mempengaruhi ramalan berkaitan

kakisan. Walaupun terdapat banyak penerbitan tentang ramalan kakisan CO2

diterbitkan namun kebanyakan model hanya tertumpu kepada algoritme yang khusus

untuk menggambarkan kesan masing-masing spesies yang berinteraksi bagi mewakili

keseluruhan kadar kakisan. Usaha ini tidaklah berapa berkesan dan ia memerlukan

bilangan uji kaji yang besar untuk memproses secara serentak semua data kakisan

yang mungkin. Bagi kajian kakisan CO2 terhadap keluli yang melibatkan kesan

interaksi maka kaedah statistik yang sistimatis yang dapat mewakili pelbagai kesan

interaksi adalah diperlukan. Pengkaedahan permukaan gerak balas digabungkan

dengan dengan teori mekanisme kakisan digunakan untuk membina model empirik

yang berkaitan dengan kesan daripada kepekatan asid asetat, suhu, dan laju putaran

pada kadar kakisan CO2 dan kakisan CO2/H2S serentak. Uji kakisan adalah

berdasarkan pada rintangan pengutuban linear dan spektroskopi impedans

elektrokimia. Keadaan aliran disimulasikan dengan menggunakan elektrod silinder

berputar. Model regresi menggunakan pengkaedahan permukaan gerak balas untuk

kesan kakisan pada karbon keluli yang melibatkan asid asetat, CO2, suhu dan laju

putaran telah berjaya dibangunkan dan diaktifkan dengan data eksperimen dan model

ramalan komersil. Dalam bentuk persamaan matematik, kesan daripada

pembolehubah bebas akan mudah dikenalpasti dan dibina. Kombinasi pengkaedahan

permukaan gerak balas adalah cekap dalam menentukan hubungan empirik antara

kebarangkalian yang diuji secara bersamaan. Seterusnya, model Pengkaedahan

permukaan gerak balas boleh digunakan untuk menentukan suhu pembekalan,

ketumpatan arus batas, dan kebersamaan aliran.

Kata Kunci: Kakisan CO2, pengkaedahan permukaan gerak balas, model kakisan.

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TABLE OF CONTENTS

Page STATUS OF THESIS i

APPROVAL PAGE ii TITLE PAGE iii

DECLARATION iv DEDICATION v

ACKNOWLEDGMENT vi ABSTRACT vii

ABSTRAK viii TABLE OF CONTENTS ix

LIST OF TABLES xiii LIST OF FIGURES xiv

LIST OF ABBREVIATIONS xvii LIST OF SYMBOLS xviii

LIST OF APPENDICES xx CHAPTER 1 ........................................................................................................... 12 INTRODUCTION .................................................................................................. 12

1.1 Background ............................................................................................... 12 1.2 Problem Statement..................................................................................... 13 1.3 Research Objectives................................................................................... 14 1.4 Scope of Study........................................................................................... 14 1.5 Organization of the Theses ........................................................................ 15

CHAPTER 2 ........................................................................................................... 16 LITERATURE REVIEW........................................................................................ 16

2.1 CO2 Corrosion ........................................................................................... 16 2.1.1 Carbonate Film Formation ..................................................................... 18 2.1.2 Transport processes................................................................................ 21 2.1.3 Factors affecting CO2 corrosion ............................................................. 21 2.2 H2S Corrosion ........................................................................................... 23 2.2.1 H2S in aqueous solution ......................................................................... 24 2.2.2 Iron sulfides formation........................................................................... 25 2.2.3 Experiments related to the role of H2S on mild steel corrosion in CO2

environments ......................................................................................... 25 2.3 Effects of HAc........................................................................................... 29 2.3.1 Introduction ........................................................................................... 29 2.3.2 Chemistry of HAc.................................................................................. 30 2.3.3 Corrosion mechanism of HAc................................................................ 31 2.3.4 Effects of HAc on carbonate film formation........................................... 32

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2.4 Prediction of CO2 corrosion ....................................................................... 33 2.4.1 Mechanistic models................................................................................. 33 2.4.2 Empirical models ................................................................................... 34 2.4.3 Semi-empirical models........................................................................... 35 2.5 Simulation of Flow Analyses ..................................................................... 37 2.5.1 The uses of rotating cylinder electrode to simulate flow induced

corrosion ................................................................................................ 37 2.5.2 Turbulent and mass transport in RCE experiments.................................. 38 2.5.3 Wall shear stress for RCE....................................................................... 40 2.6 Design of Experiment (DOE) and Statistical Modeling............................... 41 2.6.1 Design of experiments (DOE) and response surface methodology

(RSM).................................................................................................... 42 2.6.2 Types of response surface designs .......................................................... 43 2.6.3 Determination of the stationary conditions ............................................. 44 2.6.4 Model estimation.................................................................................... 44 2.6.5 Calculation of regression coefficients ..................................................... 46 2.6.6 Model accuracy measurement ................................................................ 47

CHAPTER 3............................................................................................................ 51 RESEARCH METHODOLOGY ............................................................................. 51

3.1 Design of Experiment................................................................................. 53 3.1.1 Selection of Experimental Factors ........................................................... 53 3.1.2 Variable coding and experimental design ................................................ 54 3.1.3 Setting up experimental design................................................................ 55 3.1.4 Parameters estimation.............................................................................. 58 3.1.5 Model accuracy measurement ................................................................ 59 3.2 Corrosion Experiments............................................................................... 59 3.2.1 Specimen preparation.............................................................................. 59 3.2.2 Static test................................................................................................. 60 3.2.3 Dynamic experiments.............................................................................. 61 3.2.4 Cell solutions ......................................................................................... 62 3.2.5 Composition of gases .............................................................................. 62 3.2.6 Preparation of solutions........................................................................... 63 3.2.7 Addition of HAc and acetate ................................................................... 63 3.2.8 Electrochemical measurement ................................................................. 64 3.3 Mechanistic Corrosion Model Prediction.................................................... 66 3.4 Corrosion Predictions................................................................................. 68

CHAPTER 4............................................................................................................ 69 EFFECTS OF HAc ON CARBON STEEL CORROSION IN CO2 ENVIRONMENT.................................................................................................... 69

4.1 Initial Identification of Corrosion Rate Model ............................................ 69 4.2 Design of Experiment for Analyzing Corrosion Model at pH 4 .................. 71 4.2.1 Generalization of corrosion predictions model at pH 4, HAc ................... 73 4.2.2 Prediction of CO2 corrosion model at pH 4.............................................. 73 4.2.3 Variance Analysis ................................................................................... 74 4.2.4 Model adequacy evaluation ..................................................................... 75 4.3 Verification with Experimental Data and Corrosion Prediction Software.... 77 4.4 Analysis and Interpretation of Response Surface of CO2 corrosion at pH 4. 80

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4.4.1 Effects of temperature and HAc concentration ........................................ 80 4.4.2 Effects of temperature and rotation speed................................................ 81 4.4.3 Effects of rotation speed and HAc concentration..................................... 82 4.4.4 Maximum corrosion rate......................................................................... 83 4.5 Design of Experiment for Analyzing Corrosion Rate Model at pH 5.5 ...... 85 4.5.1 Generalization of corrosion prediction model at pH 5.5.......................... 86 4.5.2 Prediction of CO2 corrosion model at pH 5.5 .......................................... 86 4.5.3 Analysis variance.................................................................................... 88 4.6 Evaluation of Model Adequacy.................................................................. 88 4.7 Verification with Experimental Data and Corrosion Prediction Software ... 90 4.8 Analysis and Interpretation of Response Surface of CO2 Corrosion at pH

5.5 ............................................................................................................. 93 4.8.1 Effects of temperature and HAc concentration ........................................ 93 4.8.2 Effects of temperature and rotation speed................................................ 94 4.8.3 Effects of HAc concentration and rotation speed..................................... 94 4.8.4 Maximum corrosion rate....................................................................... 95 4.9 Design of Experiment to Predict Corrosion Rate at varying pH.................. 96 4.9.1 Identification corrosion trend .................................................................. 96 4.10 Design of Experiment to Study Effect of pH on Corrosion Rate............... 97 4.10.1 Generalization of model....................................................................... 99 4.10.2 Prediction of CO2 corrosion model at various pH.................................. 99 4.10.3 Analysis variance.................................................................................101 4.11Prediction and Verification of Corrosion Rate at pH 5 .............................101 4.12Prediction and Verification of Corrosion Rate at pH 6. ............................103 4.13 Prediction of the Effect of pH on Corrosion rate .....................................105 4.13.1 Effect of pH and temperature on CO2 corrosion ...................................106 4.13.2 Effect of pH and HAc on CO2 corrosion ..............................................107 4.13.3 Effect of pH and rotation speed on CO2 corrosion ...............................108 4.14 Discussions: CO2/HAc Corrosion ...........................................................109 The results of the various concentrations of HAc with different variables

tested such as T and N in CO2 saturated solution are discussed in these sections below. .........................................................................................109

4.14.1 Effects of temperature and HAc concentration on corrosion rate ..........109 4.14.2 Effects of temperature and rotation speed.............................................110 4.14.3 Scaling temperature .............................................................................111 4.14.4 Effects of rotation speed on corrosion rate ...........................................113 4.14.5 Flow independent limiting current........................................................115 4.14.6 Effects of pH .......................................................................................116 4.15 Comparison between Experimental Corrosion Rates and Commercial

Predictive Models .....................................................................................116 4.16 Conclusion..............................................................................................119 4.16.1 Experimental design ............................................................................119 4.16.2 Regression model relationship .............................................................120 4.16.3 Effects of HAc, temperature and rotation speed based on RSM model .120

CHAPTER 5 ..........................................................................................................122 EFFECTS OF HAc AND H2S IN CO2 ENVIRONMENT ......................................122

5.1 Initial Identification of Corrosion Rate Model...........................................122 5.2 Design of experiment for Analyzing CO2/H2S/HAc Corrosion Model......123

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5.3 Parameter EstimationBased on mechanistic identification, the corrosion rate in CO2/H2S/HAc model was assumed to be a second-order polynomial as the best fitting. Thus, by fitting this curve to the experimental data, a regression model of the following equation was obtained: ........................ 124

5.4 Prediction of CO2 corrosion model at pH 4............................................... 126 5.5 Verification of the RSM Model with Experimental Data and Corrosion

Prediction Software.................................................................................. 127 5.5.1 Effect of HAc concentration on corrosion rate in CO2/H2S/HAc

environments........................................................................................ 127 5.5.2 Effect of temperature on corrosion rate in CO2/H2S/HAc environments. 128 5.5.3 Effect of rotation speed on corrosion rate in CO2/H2S/HAc environments129 5.6 Analysis and Interpretation of Response Surface of CO2/H2S/HAc

Corrosion ................................................................................................. 130 5.6.1 Combined effects of rotation speed and HAc on corrosion rate.............. 130 5.6.2 Combined effects of rotation speed and temperature on corrosion rate... 131 5.6.3 Combined effects of HAc and temperature on corrosion rate ................. 132 5.7 Mechanistic Study of CO2/H2S/HAc Corrosion ........................................ 133 5.8 Potentiodynamic Polarization Test ........................................................... 135 5.9 CO2/H2S/HAc Corrosion Discussions....................................................... 137 Based on data calculations using RSM model, the following sections are

discussed effects of the variables tested on corrosion in H2S/CO2 environment. ......................................................................... 137

5.9.1 Model evaluation................................................................................... 137 5.9.2 Combined effect of rotation speed and HAc .......................................... 138 5.9.3 Combined effect of temperature and rotation speed ............................... 138 5.9.4 The combined effect of HAc and Temperature ...................................... 139 5.9.5 Flow independent and flow dependent limiting current.......................... 139 5.9.6 Scaling temperature and chemical reaction limiting current in

H2S/CO2/HAc corrosion....................................................................... 140 5.9.7 Effects of H2S on CO2 corrosion mechanism......................................... 141 5.9.8 Effects of HAc on CO2/H2S corrosion mechanisms ............................... 142 5.10.1 Mechanism corrosion rate in CO2/H2S/HAc system............................. 143 5.10.2 Model regressions ............................................................................... 144

CHAPTER 6.......................................................................................................... 145 CONCLUSION AND RECOMMENDATION...................................................... 145

6.1 Conclusion............................................................................................... 145 6.2 Scope of Model........................................................................................ 146 6.3 Future Research ....................................................................................... 146

REFERENCES...................................................................................................... 135 APPENDICES……………………………………………………………………....144 LIST OF PUBLICATIONS…………………………………………………………152

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LIST OF FIGURES

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CHAPTER 1

INTRODUCTION

1.1 Background

Carbon dioxide (CO2) corrosion has always been an important corrosion management

issue in oil and gas industry. Although, the understanding of pure CO2 corrosion is

well accepted, the corrosion mechanism with the presence of other species such as

acetic acid (HAc) and hydrogen sulfide (H2S) is unclear [1-5]. The CO2 corrosion

problem is further complicated as the corrosion can be influenced not only by various

reservoir species but also operational parameters such as temperature, pH, and flow

condition. The possible interactions between various species and operating condition

pose a challenge in the CO2 corrosion prediction. The accuracy of a corrosion

prediction hinges on realistic treatment of the possible interactive effects between

these chemical species and operational variables.

In fact, corrosion modeling in a CO2 containing environment has been studied

extensively for the last decades. Many published papers on CO2 corrosion prediction

studied the effects of species like H2S and HAc in conjunction with other operating

parameters including temperature, pH, and flow condition. Most of the prediction

models rely on specific algorithms to combine individual effect of the interacting

species to represent a cumulative total corrosion rate. The individual effect was

determined from the experimental routine of holding constant certain variables and

changing the values of another variable. This experimental method is inefficient and

needs a large number of experiments to process all possible corrosion data.

Hence, this complex nature of CO2 corrosion poses a challenge to construct CO2

corrosion model efficiently. Existing empirical models have shown acceptable results

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in predicting the individual effects but apparently not qualified to predict

corrosovity of the system arises from simultaneous interactions of different variables.

The need to represent the interactive effect of several key parameters in CO2

corrosion is undoubtedly important in the corrosion study.

The simultaneous effects of many variables in the CO2 corrosion could be

optimized by using a statistical methodology such as design of experiment

methodology. A systematic statistical method can represent the multitude of the

interactive effects of variables considered.

1.2 Problem Statement

A multitude of factors can affect CO2 corrosion, particularly when HAc and H2S

species are present. The presence of HAc and H2S bring complexity into the

experimental methodology to predict corrosion rate based on an empirical method.

Using a normal empirical method, an attempt to model possible interactive effects

between the species and the operational conditions, not only requires a large number

of experiments but most important the resultant modeling could not be statistically

validated. Thus the empirical relationship obtained through best fit regression, for

example of many empirical CO2 corrosion models, tends to misinterpret the real

corrosion kinetics. Furthermore, the resultant models were not usually based on

theoretical basis to guide data fitting to formulate the regression model. Moreover,

there are limited expressions in the literature to quantify the mixed variables

simultaneously and no expressions were previously developed to express the

corrosion model in CO2/H2S/HAc environment. Considering these limitations, it is

important to develop a CO2 corrosion model founded on fundamental theory and

systematic statistics approaches that expresses relationship between the reservoir

species (HAc, H2S) and operational conditions (temperature, pH, flow condition).

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1.3 Research Objectives

The main objective of this research is to predict corrosion rate of carbon steel due to

the combined effect of H2S/HAc species at various operating conditions in CO2

environment, using the response surface methodology (RSM). The work has been

carried out to meet the following specific objectives:

Develop empirical models of carbon steel corrosion rate in aqueous CO2

solutions and CO2/H2S environments at various HAc, pH, temperature and

flow condition.

Investigate the effects of HAc in combination with pH, temperature, and flow

condition simultaneously on carbon steel corrosion in CO2 environment.

Investigate the effects of HAc acid in combination with pH, temperature, and

flow condition simultaneously on carbon steel corrosion in CO2 and H2S

environment.

1.4 Scope of Study

The research is on prediction of the corrosion behavior of carbon steel in CO2

environment with the presence H2S, and HAc at different pHs, temperatures and flow

conditions. The analyses of the model was based on mechanistic theory, published

experimental data, and commercial corrosion predictive software. The Linear

Polarization Resistance (LPR) technique was used to measure the polarization

resistance (Rp) and calculate corrosion rate. The corrosion rate and mechanism was

determined using Electrochemical Impedance Spectroscopy (EIS) technique. The

parameters used are HAc concentration, H2S concentration at various temperature, pH

and flow conditions. Rotating cylinder electrode (RCE) equipment was used to

simulate flow condition in pipeline.

The empirical modeling is based on the RSM technique that relates effects of

HAc, temperature, and flow condition on CO2 and CO2/H2S corrosion rate

simultaneously

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1.5 Organization of the Theses

This dissertation consists of six chapters. Chapter 1 describes the research background

related to CO2/H2S/HAc corrosion of carbon steel. It gives an overview of oil field

environments, corrosion predictions models, problem statement, research objectives,

and scope of study.

Chapter 2 contains extensive literature review on CO2 corrosion. It also describes

literature review about H2S, HAc and parameters influencing corrosion mechanism.

The literature review on design of experiment is also presented in this chapter. In

addition Chapter 2 also discusses predictive models developed by researchers and

their comparison with published papers for justification.

In Chapter 3, detail of material specification, material preparation, corrosion

testing methodology, and experimental design methodologies were explained.

Analyses of the results are presented in Chapter 4 and Chapter 5. Chapter 4

presents results and discussion relating effects of HAc in CO2 gas condition, while

Chapter 5 discusses effects of HAc in CO2/H2S condition. In this study, published

papers, corrosion experimental data from researchers and from experiments were

compared and discussed to verify the models.

Finally, Chapter 6 contains conclusion. The conclusion summarizes the results

and compares the models to determine the most appropriate model for the

CO2/H2S/HAc corrosion pattern.

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CHAPTER 2

LITERATURE REVIEW

2.1 CO2 Corrosion

Corrosion mechanism of mild steel in the presence of CO2 has been widely reviewed ,

particularly in relation to the oil and gas application [6, 7]. The mechanism

influencing CO2 corrosion, the effects of main parameters such as HAc concentration,

temperature and flow conditions have been identified. In CO2 corrosion prediction,

theoretical analysis involving chemistry, electrochemistry, mass transport processes

and various possible reactions should be considered. Researchers have investigated

various variables that affect the corrosion rate in order to develop a prediction model.

However, the accuracy of existing CO2 corrosion model is still debatable and at worst

contradictory. Thus, further researches on the effects of parameters such as

temperature, HAc and flow conditions in CO2 corrosion are still open to explore.

Several CO2 corrosion models were based on experimental and field studies. The

study in CO2 corrosion conducted by C. deWaard and Milliams [8] has become a

foundation for further studies on the CO2 corrosion phenomenon. The latest

publications of CO2 corrosion mechanism was proposed by Nesic et al. [9]. Based on

their model, CO2 corrosion covers anodic dissolution of iron and cathodic evolution

of hydrogen which involve the electrochemical reactions at the steel surface, transport

of reactive species between the metal surface and the bulk, and the chemistry in the

bulk solution. The following is a summary of the mechanism processes in CO2

corrosion as proposed by Nesic and Miran [10]. At the cathodic site, CO2 dissolves

into the water phase and becomes hydrated to form carbonic acid as represented by

Equations 2.1 and 2.2.

CO2 (g) ↔ CO2(aq) (2.1)

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CO2 (aq) + H2O ↔ H2CO3 (2.2)

Then, carbonic acid dissociates by further reactions depending on the pH of the

solution. At pH 4 or lower, carbonic acid dissociates into bicarbonate ions and

carbonate ions in two steps (Equations 2.3 and 2.4).

H2CO3 ↔ HCO3- + H+ (2.3)

HCO3- ↔ CO3

2- + H+ (2.4)

At pH values between 4 and 6, carbonic acid dissociates to produce bicarbonate

ions. The direct reduction of carbonic acid to produces hydrogen gas as described in

Equations 2.5.

2H2CO3 + 2e-→ H2 + 2HCO3- (2.5)

At higher pH around 5, it was proposed that the bicarbonate ion reduces into

carbonate ion and releases hydrogen gas as expressed in Equation 2.6:

2HCO3- + 2e- → H2 + 2CO3

2- (2.6)

At higher pH and pressure, the evolved hydrogen can adsorb to the diffusion layer

according to Equation 2.7.

H+ + e- + H(ads) →H2(ads) (2.7)

At pH more than 6, the cathodic rate is also controlled by the production of

carbonic acid (Equations 2.8).

HCO3- + H2O → H2CO3 + OH- (2.8)

It was suggested that H+ ions are the dominant species promoting corrosion.

H+ ions are able to diffuse to the metal surface through boundary layer. On the metal

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surface, the H+ ions participate in hydrogen evolution reaction. These additional

charge transfer reactions are suggested as the factors governing the corrosion rate

(Equations 2.9 and 2.10).

H+ + e- → H(ads) (2.9)

H(ads) + H(ads) → H2(ads) (2.10)

At the anodic site, oxidation reaction occur to form ferrous ions (Fe2+). The

general reaction is shown in Equations 2.11.

Fe → Fe2+ + 2e- (2.11)

Bockris [11] proposed anodic dissolution of Fe ions (Fe2+) according to the

following mechanism (Equations 2.12 and 2.14) :

Fe + OH- → FeOH + e- (2.12)

FeOH → FeOH+ + e- (2.13)

FeOH+ → Fe2+ + OH- (2.14)

This steady state anodic reaction that brings the variation to Tafel slopes was also

discussed by Videm [12]. However, according to Nesic et al. [13], the presence of

CO2 does not have any effects on the anodic dissolution of iron and Tafel slopes due

to effects of catalyzes of chemical ligand in the metal surface.

2.1.1 Carbonate Film Formation

CO2 corrosion reaction leads to the formation of iron carbonate (FeCO3) film. This

corrosion film may be protective or non-protective depending on the conditions of the

environment, such as pH, CO2 pressure, temperature and flow conditions, and ferrous

ions concentration. The corrosion product of the bicarbonate ion can increase pH of

the solution to reach its solubility limit [14]. At temperature less than 60oC, protective

film does not form due to the solubility of FeCO3 is high and the precipitation rate is

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slow [15]. However, at temperatures more than 60oC, the high precipitate rate, the

film is protective that can reduce corrosion rate substantially [15].

The formation FeCO3 occurs through two processes as shown in Equations 2.15 –

2.17. When ferrous ions react with bicarbonate ions, iron bicarbonate forms, which

subsequently dissociates into iron carbonate [16].

Fe2+ + CO32- → FeCO3 (2.15)

Fe2+ + 2HCO3- → Fe(HCO3)2 (2.16)

Fe(HCO3)2 → FeCO3 + CO2 + H2O (2.17)

The FeCO3 formation will precipitate when the local concentration of Fe2+ and

CO32– species exceeds the solubility limit K sp [17].

The solubility limit K sp is defined as:

6063.00115.00182.013.10

ITK sp (2.18)

T is temperature in ºC and I is ionic strength in mol/L. The ionic strength is defined

as:

i

ii zcI 2

21 (2.19)

Where c is species concentration and z is the species charge.

Typically, in order to obtain significant rates of film formation, high temperature

(>60°C) and considerable supersaturation (SS) is required. Conditions favoring the

formation of the protective iron carbonate scale are in high temperature and high pH.

Dependency on temperature and ion activities of the bulk saturation value for iron

carbonate, SS (FeCO3), is calculated using the equation 2.24 for solubility product

[18]. Johnson and Tomson [19] developed a model for the precipitation kinetics of

FeCO3 in which the precipitation rate (in kmol/Jm3s) as follows:

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t

FeRFeCO

2

3 (2.20)

25,0 1 SSKVAK spr (2.21)

Where, Kr i s the temperature-dependent rate constant, A/V is the

surface/volume ratio, Ksp, the solubility product of FeCO3 and SS is supersaturation

level defined as [18]:

sp

S KCOFe

S

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2

(2.22)

Equation 2.22 is based on the assumption that the precipitation rate of FeCO3

in corrosion systems is controlled by kinetics and not by nucleation. Another

formula to calculate FeCO3 precipitation has been proposed by Johnson and Tomson

[19], and Hunnik et al [16]. with different expressions for the precipitation (crystal

growth) rate. According to Johnson and Tomson [19]:

25.00.1238.54

)1(3

SspRT

FeCO SKAeR (2.23)

According to Hunnik, et al.[16]:

)1)(1( 18.1194.52

3

SSsp

RTFeCO SSKAeR (2.24)

Where RFeCO3 is precipitation growth, A is the surface area available for

precipitation per unit volume, Ksp is the precipitation rate constant, R is universal gas

constant, T is temperature, and SS is super saturation. From the two different rate of

precipitation equations, it can be distinguished that the Johnson and Tomson equation

(2.23) is suitable for very low levels of supersaturation that represents a nucleation

growth. While Hunnik equation is used for large supersaturations of a film

precipitation [17, 18].

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2.1.2 Transport processes

It has been known that during electrochemical processes, there is a transport of certain

species in the solution. At metal surface, ferrous ions (Fe2+) will increase while other

species will be depleted [7, 20]. The concentration of the species will be higher near

the metal surface than in the bulk solution. This concentration differences will lead to

molecular diffusion of the species toward and away from the surface. In cases when

the diffusion processes are much faster than the electrochemical processes, the

concentration change at the metal surface will be small [21].

Many of the dissolved species in CO2 solutions are controlled by electrically

charged ions and have different diffusion coefficients. This means that they diffuse

through the solution with different speeds depending on the potential difference.

Consequently, any diffusion occurring as a result of the existence of concentration

gradients will tend to change the charges ions [21]. In general, transport processes that

occur in solution containing CO2 involves convective diffusion, molecular diffusion

and diffusion via corrosion film. The film acting as a barrier on the metal surface

depends on time, hydrodynamic stresses, chemical reaction, precipitation rate, change

of mass scale removal of the outer scale and material microstructure [22 - 26].

2.1.3 Factors affecting CO2 corrosion

There are many factors that can influence both thermodynamics and kinetics of CO2

corrosion. Main factors as experienced by field operations, such as operating

conditions and solution chemistry, have shown a significant impact on corrosion

mechanistic model and caused different types of corrosion morphology. In the

following sections, several main factors that govern the corrosion rate are discussed.

2.1.3.1 pH

pH is an important parameter for any corrosion process. The pH is determinated by H+

ions concentration which is influenced by temperature, pressure, and ionic strength.

Dissolved iron bicarbonate will also contribute to an increase in pH of the solution

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[27]. Normally, an increase in pH will cause the film to become thicker, denser and

protective that relates to the passivity [29].

2.1.3.2 Temperature

Temperature has been identified to affect corrosion rate. The role of temperature in

influencing corrosion rate is related to corrosion kinetic; diffusion coefficient and

activation energy of species. At the higher temperature, diffusion coefficient of

species is higher that can accelerate the species to corrode the metal surface.

Temperature facilitates conditions for formation of the protective carbonate layers and

affects lower corrosion rate. This temperature is called scaling temperature that is

affected by flow rate and pH, where higher flow rate and lower pH will produce

higher scaling temperature. The correlation between scaling temperature and those

variables have been studied by researchers [30, 31].

2.1.3.3 Effects of CO2 partial pressure

Corrosion rate will increase when the partial pressure of CO2 increases. At higher

partial pressure of CO2, CO32- io ns concentration will have higher super saturation

(at the high pH) which leads to increase corrosion rate. An increase in the total

pressure of the gas will lead to an increase in corrosion rate too, especially for the

non-ideal gas at high pressure [28].

2.1.3.4 Effect of Fe2+ concentration

The effects of Fe2+ ions on corrosion rate are influenced by its ability to form iron

carbonate. It has been commonly known that solid iron carbonate scale precipitates on

steel surface when the concentrations of Fe2+ and CO3 2- ions in the CO2 water

solution exceed the solubility limit. The increase of Fe2+ results in higher

supersaturation, which consequently accelerates the precipitation rate and leads to

higher surface scaling tendency to form a corrosion product films [21]. Protective

films will not form when the scaling tendency is very low although Fe2+ has achieved

23

a saturation value. In this condition, the iron carbonate film that forms is very porous

and is not protective, which will not be effective in reducing corrosion rate [16].

2.1.3.5 The effect of flow conditions

The effect of fluid velocity on corrosion rate is associated with higher turbulence and

mixing in the solution. This mixing affects the corrosion rate and the iron carbonate

film formation. High velocity leads to an increase in corrosion rate as the transport of

cathodic species toward the steel surface is enhanced by turbulent flow. At the same

time the transport of Fe2+ ions away from the steel surface is also increased, leading to

a lower concentration of Fe2+ ions at the steel surface. This results in a lower surface

supersaturation and slower precipitation rate. Both contribute to less protective films

formed at high velocities. More details about the effects of velocity on corrosion rate

are described in the subsequent discussion as reported by Silverman et al. [32-38].

The degree of corrosiveness caused by velocity is also related to crude oil type,

multiphase condition and water cut. Those parameters determine how well the water

can wet the steel surface and lead to govern corrosion rate [39 - 43].

2.2 H2S Corrosion

Incorporating the effects of H2S gas in corrosion calculations is important for the

prediction of CO2 corrosion since many of the oil fields around the world contain this

acid gas [1, 3, 4]. The CO2 corrosion mechanism will change if H2S gas exists in the

system. Intensive studies have been conducted to study the effect of H2S gas in CO2

system. As discussed in many published papers, the complex chemistry and

mechanism of corrosion process make it difficult to predict CO2 and H2S corrosion

processes. The corrosion process may involve a combination of reactions between

corrosion rate and film formation rate. Thus, further research is needed to investigate

how H2S gas affects corrosion rate in CO2 system.

24

2.2.1 H2S in aqueous solution

The dissociation of hydrogen sulfide in water involves a series of chemical reactions

as described from Equations 2.25 to 2.29. The proposed chemical reactions steps are

[44]:

i. H2S dissolution

H2S(g) ↔ H2S(aq) (2.25)

ii. H2S dissociation

H2S(aq) ↔ HS- (aq) + H+

(aq) (2.26)

iii. HS- dissociation

HS-(aq) ↔ H+

(aq) + S2-(aq) (2.27)

iv. H2S Reduction

2H2S(aq) + 2e- → H2(g) + 2HS-

(aq) (2.28)

v. FeS formation by precipitation

Fe2+(aq) + S2-

(aq) ↔ FeS(s) (2.29)

At pressures less than 200 kPa, the solubility of molecular H2S in water is given by

Henry's law as:

MH2S H = YH2S P (2.30)

Where YH2S is the mole fraction of hydrogen sulfide in vapor, P is the total pressure,

MH2S is the molality of the molecular form of hydrogen sulfide in water (moles per

kilogram of water), and H is Henry's constant.

The reactions of H2S in aqueous vary with pH. At acidic solutions, the dominant

sulfide species is molecular H2S. At pH of about 6, the solutions will contain bisulfide

ions. The higher pH will result in the formation of bisulfide will increase. At pH of

around 7, the amount of H2S molecular and bisulfide forms is similar [45].

25

2.2.2 Iron sulfides formation

In H2S corrosion system, there are different possibilities of iron sulfide formation in

aqueous solution [46]. The formation of solid film on the surface is due to anodic

dissolution of iron. Ferrous ions dissolve into solution and react with sulfide ions

(FeS) in the solution, hence no film of corrosion product on the surface. The

formation of sulfide can also by mixing reaction between ferrous ions that react on the

surface and in solution. Those film formations bring different film porosities of FeS.

The porous surface facilitates the cathodic reaction and creates anodic dissolution of

iron that affects to the corrosion rate [46]. The types of FeS are influenced by

temperature and H2S activity [45]. Based on kinetics theories, several types of FeS

are commonly found in oil field corrosion are pyrite (FeS2), pyrrhotite, and

mackinawite.

When H2S gas presents with CO2 gas, there will be a growth competition between

FeCO3 and FeS films which affects to the corrosion rate. Nesic et al. [47] constructed

a model to simulate film formation growth of CO2/H2S competition reactions. From

the simulated model, they identified that the growth of film formation containing

H2S/CO2 gas, initially, is started by FeS film formation. Then, the FeCO3 film

becomes thicker and denser at the metal/film interface due to an increase in pH and

Fe2+ concentration.

2.2.3 Experiments related to the role of H2S on mild steel corrosion in CO2

environments

The role of H2S in CO2 corrosion was studied by Brown [44]. In his experiment, he

found that the corrosion rate in CO2 saturated water will increase in the presence of

small H2S concentration of less than 30 ppm. However, he also observed a reduced

corrosion rate in 100 ppm H2S concentration, and pH solution < 5. In single phase and

multi phase flow experiment, the scale produced was adherent and protective enough

to retard corrosion attack. The scale was more protective when temperature was

increased to 80oC.

26

The findings by Brown was supported by Lee [18]. Lee set the experimental

variable as; temperature 20oC, pH 5, partial pressure 1 bar, flow rate 1000 rpm,

concentration of H2S in CO2 in the range of 0 - 340 ppm. All of the experiments

indicated that very small of amount of H2S (10 ppm) in phase gas lead to rapid

reduction of the corrosion rate. Based n the SEM observation, they found that the

scale formed on the surface that inhibited corrosion rate have a mackinawite structure.

They stated that the mechanism of scale growth was not of mass-transport control, but

rather a charge transfer controlled. Brown and Lee revealed that at 20oC – 60oC, a

competition to form the protective film takes place between H2S and CO2 corrosion

mechanism.

In experimental research work done by Agrawal et al. [48], observed that the

phenomena of accelerated corrosion in a CO2 and H2S environment occurs at low H2S

concentration. They also found that there was a strong correlation between the

corrosion rates and the temperature. In the range of H2S concentration studied, the

corrosion rate showed a polynomial curve with increasing the temperature.

Andrzej et al. [49] proposed a model involving thermophysical properties,

electrochemical properties, and scale effects to predict corrosion rate. They reported

significant drop in corrosion rate for partial pressures of H2S ranging from 2.10- 6 to

10-4 bar and the rate reached a plateau in a relatively wide range of H2S partial

pressures above 10-4 bar. Reduction in corrosion rates has been reported when the H2S

partial pressure exceeds 10-3 bar in some systems. At substantial H2S partial pressures

(above 10-2 bar), the aqueous H2S, and HS- species become sufficient to increase the

corrosion rate. That observation is supported by Chengqiang [3] who found that

corrosion rate in CO2 system will decrease quickly as compared to sweet corrosion in

low concentration of H2S.

Kvarekval et al. [50] worked with 150 – 450 ppm of H2S. Experiments with up to

2 bar CO2 and temperatures up to 80°C resulted in slightly higher corrosion rates than

in corresponding experiments without H2S. The corrosion rates were in the range of

0.1-2 mm/y. In an experiment with 0.5 mbar of H2S at a CO2/H2S partial pressure

ratio of 4500, both iron sulfides (FeS) and iron carbonates (FeCO3) were detected on

the steel surface. The mixed sulfide/carbonate films were 30-80 µm thick.

27

Experiments with CO2/H2S ratios of 1200-1500 resulted in formation of thin iron

sulfide films (1- 10 µm ) on the corroding surfaces. No iron carbonates were found in

corrosion product films formed at CO2/H2S ratios below 1500.

Singer et al. [51] found that trace amounts of H2S greatly retards the CO2

corrosion with general corrosion rates usually 10 to 100 times lower than their pure

CO2 equivalent. The most protective conditions were observed at the lowest partial

pressure of H2S. However, corrosion rate increased when more H2S was added. The

presence of trace amounts of H2S (0.004 bar) in the CO2 environment sharply

decreases the corrosion rate by two orders of magnitude. As the partial pressure of

H2S is increased to 0.13 bar, the tendency is reversed and the general corrosion rate

increased by an order of magnitude.

Carew et al. [43] observed a rapid and significant reduction in the CO2 corrosion

rate both in single and multiphase flow in the presence of 10 ppm H2S. At higher H2S

concentrations (up to 250 ppm) the trend was reversed and a mild increase of the

corrosion rate was observed. An acceleration of CO2 corrosion rate was observed at

60°C, 0.79 MPa CO2 at multiphase flow with only 3 ppm H2S. Similar result was

reported by Zhang [52] who discussed effects of high H2S partial pressure on

corrosion of API-X52 and X60 pipeline steels. The results showed that the corrosion

rate of the two steels increased with the H2S partial pressure at the temperature of

60oC. General corrosion was at the H2S partial pressure of 0.15MPa, 0.33MPa and

1.5MPa, and at the H2S partial pressure of 2.0MPa, localized corrosion was observed.

Schmitt et al. [53] stated that a change in pH from 4 to 6 had only little effect on

the corrosion rate, and at pH 6, 60 °C and 25 ppm H2S, protective corrosion films

were formed and no localized corrosion were observed [54]. The effect seems to

vanish at higher pH values (5.5-7) and higher temperatures (>80°C), when a

protective film is formed. They concluded that an increase of the CO2 partial pressure

in the same flow system from 3.8 to 10.6 bar reduces the maximum corrosion rates

from about 15 to 0.2 mm/y (Fig. 6) [55] under conditions when semi-protective films

are formed, e.g. in the pH range below 5.2.

Kermani [56] expressed a reduction of corrosion rate due to formation of FeS film

by a formula below.

28

FH2S = 1 / (1 + 1800 (pH2S/pCO2)) (2.31)

Where FH2S is scaling factor for corrosion reduction due to FeS precipitation.

Further, in combining with the presence of CO2 and H2S, there is a competitive

interaction between FeCO3 and FeS corrosion products that may lead to localized

corrosion. Subject to the type and nature of the corrosion product, H2S may lead to an

increase in CO2 corrosion until certain concentration threshold after which can reduce

corrosion rate.

On further research, Papavinasam et al. [57], concluded that corrosion rate

increased both with H2S partial pressure and with rotation speed up to approximately

500 rpm. Beyond 500 rpm, the synergism was lost and the corrosion rate decreased (at

20 psi CO2). At 100-2000 rpm, corrosion rate increased due to H2S pressure until 75

psi, then decreased after that (at 20 psi CO2). At 25 – 100 psi H2S pressure, corrosion

rate decreased with the rotation speed until 500 rpm, and increased beyond this value

(at 20 psi CO2).

In combination with CO2, corrosion rate of H2S showed different phenomena

compared to without CO2 as reported by Makarenko et al. [58]. With CO2, the

corrosion process is accelerated by cathodic reaction of hydrogen ion reduction. It has

been proven that CO2 corrosion of carbon steel increases by 1.5–2 times with increase

of H2S content in the mixture (p H2S<0.5 MPa) in the temperature range 20–80°C.

Further increasing in H2S content (p H2S≥0.5–1.5 MPa), the corrosion rate will

decrease, especially in the temperature range 100–250°C, because of the influence of

FeS and FeCO3 on corrosion. It may relate to formation of protective film [58].

From the literature review, it is found that the mechanistic equations by Nesic et

al. [54] is the feasible theories for describing effect of H2S on CO2 corrosion. It

should be noted here that, based on the theories, the corrosion rate can be calculated

by considering overall individual anodic/cathodic reactions involving in the systems.

In general, the results are considerable. However, the reasons behind effects of H2S on

CO2 corrosion are not fully understood, especially for the complex parameters.

Current laboratory research is conducted based on individual anodic/cathodic

29

experiments using specific parameters which are not an accurate enough to represent

multi interaction effects. Almost all researchers, in their design experiments, did not

consider effect of H2S/CO2 with varying temperature and flow on corrosion rate

simultaneously. In fact that the effects of H2S, in CO2 corrosion, are controlled by film

formation or activation process depends on the H2S concentration, temperature, HAc

(as a representative of main component in reservoir) and flow condition. Mostly, the

researchers agreed that at the higher H2S concentration (>250 ppm), the corrosion rate

will increase. But, they did not account how the corrosion behavior will change when

the various values of temperature, HAc concentration and rotation speed were

involved simultaneously. Studying simultaneous effects of variables will be useful to

describe not only individual effects but also synergistic interaction of variables tested.

The synergistic interactions of the corrosion reactions among the variables are

important in CO2/H2S corrosion prediction, but not yet fully understand.

Since no CO2/H2S corrosion experiments consider parameters effects simultaneously

in the modeling, and there are possibilities interaction effects that bring the complexities,

a new experimental design technique should be conducted to investigate the following

phenomena:

How does the corrosion rate change when the corrosion parameters was involved

in the experiments simultaneously?

How does the model of corrosion rate behaves when multi interaction conditions

occurs?

Will each anodic/cathodic reaction have linear correlation with corrosion rate

when experiments are conducted simultaneously?

2.3 Effects of HAc

2.3.1 Introduction

HAc is a possible catalyst in the CO2 corrosion. The failures were reported in many

cases and the effects of HAc on corrosion rate have been studied by many researches

[59-62]. The effect of HAc on CO2 corrosion is to either increase or decrease

30

corrosion strongly depending on pH and temperature. However, research on the

combined effect of H2S and HAc in CO2 system is still limited. In the literature, the

effects of those factors are debatable and sometime contradictory. Therefore, it is very

important to improve the understanding of carbon steel corrosion related to CO2/H2S

and HAc.

2.3.2 Chemistry of HAc

The structural formula of HAc is CH3COOH. It is a weak acid that does not

completely dissociate in aqueous solutions. It has been reported that free HAc can

cause an increase of corrosion rate [60]. The mechanism of dissolved HAc in CO2

corrosion can be correlated to the concentration of undissociated HAc present in the

brine [62 - 63]. Laboratory tests conducted by George et al. [62] have validated that

dissociated acid can alter the corrosion rate in CO2 environment. The dissociation of

HAc in water occurs according to the Equations 2.32 below [17]:

HAc(aq) + H2O ↔ H3O+(aq) + Ac-

(aq) (2.32)

The aqueous HAc, then partly dissociation into hydrogen and acetate ions (Equations

2.33 and 2.34).

HAc(aq) ↔ H+(aq) + Ac-

(aq) (2.33)

H+(aq) + e- → ½ H2(g) (2.34)

The equilibrium constant for HAc dissociation, KHAc is:

KHAc= HAc

AcH

(2.35)

In a CO2 environment with the presence of HAc, the overall corrosion reaction for

carbon steel is shown in Equations 2.36 and 2.37:

Fe + H2CO3 → FeCO3 + H2 (2.36)

31

Fe + 2HAc → Fe(Ac)2 + H2 (2.37)

The dependency of HAc equilibrium constant on temperature is expressed in the

following formula [17]:

26107856.23013491.066104.6(10 KK TxT

HAcK (2.38)

Where TK is temperature in Kelvin. The rate of reaction involving CO2 and HAc acid

is believed to be limited by the preceding slow hydration of CO2 (Equations 2.39)

[17]:

CO2 + H2O → H2CO3(aq) (2.39)

The reaction mechanism and kinetics of the overall reactions are influenced by HAc

concentration, CO2 partial pressure, pH, and water contaminants.

2.3.3 Corrosion mechanism of HAc

The effect of HAc on the corrosion of mild steel has been studied by a number of

researchers. Crolet and Bonis [64] made the point that CO2 induced acidification also

can cause partial re-association of anions. Such weak acids then will increase the

oxidizing of H+ by raising the limiting diffusion current for cathodic reduction. The

presence of this acid also will tend to solubilise the dissolving iron ions.

The electrochemical behavior of carbon steel on the additions of HAc has shown

that the presence of HAc in the solution decreases pH, increases the cathodic limiting

current, and decreases Ecorr. In this condition, the cathodic reaction will become the

rate determining step. The limitation is due to diffusion of proton to the steel surface

rather than electron transfer. In general, it has been agreed that HAc can increase the

cathodic reaction rate (hydrogen evolution reaction) if the concentration is significant.

Garsany et al. [65] published work using voltametry to study the effect of acetate

ions on the rates and mechanisms of corrosion using a rotating disc electrode (RDE)

32

on film-free surfaces. They found a figure that can be attributed to hydrogen ion and

HAc reduction on steel surface. They argued that since HAc dissociation can occur

very quickly, it is not possible to distinguish the reduction of hydrogen ions from

direct HAc reduction at the electrode surface. They argued that the increase of

corrosion rate of HAc in CO2 environment must be proportional to the concentration

of undissociated HAc in the brine. They emphasized that the electrochemistry of HAc

at steel cannot be distinguishable from free proton because of its rapid dissociation.

This conclusion was recorded after they used a cyclic voltammetry to study the effect

of Ac- ions on the rate of corrosion using rotating disk electrode.

Crolet et al. [64] suggested that the presence of HAc inhibited the anodic (iron

dissolution) reaction at low concentrations of HAc (6-60 ppm). They found that the

increase of corrosion rate in the presence of HAc was due to an inversion in the

bicarbonate/acetate ratio. At this inversion point, HAc is the predominant acid

compared to carbonic acid and is therefore the main source of acidity.

Although the data of HAc on corrosion rate has been provided by many published

work in the literature and field experience as presented above, the data did not predict

the interactions effects of the HAc with various conditions clearly. In fact, the

prediction becomes complicated when temperature and flow condition was considered

as HAc that could interfere in the FeCO3 film formation. This complexity becomes

another unknown problem to solve since there is no published work carried out to

study the interaction effects.

2.3.4 Effects of HAc on carbonate film formation

An investigation of HAc role in corrosion rate on film formation was done by George

[62]. The experiment succeeded in creating a film on the steel surface after exposing

the specimen for three days at a temperature of 80oC and high pH using LPR and EIS

corrosion measurement methods to identify the effect of HAc on the cathodic and

anodic reactions of CO2 corrosion. He concluded that HAc does not affect the charge

transfer mechanism of cathodic reaction but affects the limiting current. At room

temperature (22oC) the HAc acts as a source of hydrogen ions.

33

Vennesa et al. [66] observed that the role of HAc can retard the time to reach

scaling temperature due to an increase in the area of corrosion. This argument was

supported by experimental observations which showed a reduction in corrosion rate in

experiments without acetate ion. There was an evidence that acetate ion can attack

existing iron carbonate films and make them thinner. If the attack was localized, it

would result in local film thinning, thus causing pitting corrosion. Hedges [22]

published results on the role of acetate role in CO2 corrosion. Experiments using both

HAc and sodium acetate (NaAc) as a source of acetate ions in various media (3%

NaCl and two synthetic oilfield brines) were performed using rotating cylinder

electrodes. Both sources of acetate ions were shown to increase the corrosion rate,

while HAc decreased the pH and NaAc increased the pH. The increased corrosion

rates were attributed to the formation of thinner iron carbonate films since acetate ions

have the ability to form iron acetate and transport iron away from the steel surface.

2.4 Prediction of CO2 corrosion

Since CO2 corrosion involves multi species corrosion mechanisms, numerous

corrosion predictions models with different parameters and using different approaches

have been developed [10, 67, 68]. Each model predicts corrosion rate in different

ways. Researchers used parameters and formula from literatures, experimental data

and their own experiences to construct corrosion model. The results predicted by the

corrosion models may differ and sometimes contradicting. Since different results may

be obtained for the same case, therefore the understanding of the basis of model

development is required in order to interpret the corrosion data meaningfully. Nesic et

al. [10] have classified the model into three categories: mechanistic, semi-empirical,

and empirical model.

2.4.1 Mechanistic models

Mechanistic models use theoretical background to describe the mechanisms of

reactions. It has a strong theoretical background and physical results. The main

concepts of mechanistic models are the interrelation between chemical reactions and

34

physical changes. The mechanistic corrosion model is developed using information of

standard state properties of all species, Gibbs energy and thermodynamics theory,

which are applied to predict the concentration and activities of the species. It covers

electrochemical reactions and diffusion process. In the case of corrosion occurring at

the metal surface, it can be identified as convective diffusion, molecular diffusion, or

diffusion via solid film.

Mechanistic model can also be formulated from electrochemical reactions where

electrons are transferred between molecules which are called oxidation/reduction

reactions. The Tafel diagram can be applied to investigate corrosion mechanisms that

occur by electrochemical processes at the metal surface and transport processes for

the chemical species involved. The model focuses on cathodic and anodic reactions

which occur in the system involving several species. The mechanism of anodic

dissolution depends on the dissolution rate and on the activity of hydroxide ions.

While cathodic processes are related to the reduction of the species involved.

Examples of mechanistic corrosion models are de Waard and Milliams models [8],

Lee [18] and Nesic et al. [10].

Because of the large number of variables involved and their complex interactions

may occur, the mechanistic model is not simple and over simplified. Parameters

assumed and variables considered were not accurately modeled. Therefore, the

mechanistic corrosion need to be further evaluated in laboratory for reliable

performance.

2.4.2 Empirical models

Empirical corrosion prediction models are developed based on best-fit parameter in

experimental regression. Empirical models are usually developed by involving several

fixed variables. However, in subsequent considerations, other factors are added to

give a better correction factors. There have been a number of empirical models

developed based on field experience and laboratory data. French et al. [69] have

investigated corrosion film characteristics of gas wells containing CO2 in the range

temperature from 20 to 149oC. Smith [70] developed a model for a slightly sour

system. The model shows various corrosion products of steel formed in the presence

35

of CO2 as a function of temperature and partial pressure of H2S. Nyborg [71] has

recently reviewed an empirical model to estimate the corrosion rate using two

variables; temperature and partial pressure of CO2. Norsok M-506 [72] is an empirical

model based on experiments conducted in a single phase water flow loop. The

experiment data cover effects of pH, CO2 fugacities, wall shear stresses,the

temperature range from 5oC to 150oC. The newest empirical model of CO2 corrosion

was reported by Martin [60] and Ismail [61]. However, the use of use pure empirical

model is not efficient. Empirical model needs a large and reliable experimental

database that takes long duration time and costly.

2.4.3 Semi-empirical models

Semi empirical models are developed using parameters and formula from literatures

and based on the researchers’ own experiences. There are many equations that

predicts the corrosion rate in CO2 environments. These include the de Waard [72] and

its many subsequent derivatives, Yuhua [74], Vera [39] and George et al. [62]. All of

these were developed based on different systems and assumptions. Some corrosion

predictions softwares that have been developed based on semi-empirical approach are

discussed herewith.

ECE (Electronic Corrosion Engineer)

ECE [75] program software calculates corrosion rate based on the modified de

Waard and Milliams method [8]. ECE model includes oil wetting correlation based on

field correlation. For low horizontal flow velocities < 1 m/s, the Foil =1. ECE proposes

a corrosion prediction expression as follows:

mr

cor

VV

V11

1

(2.40)

Where, Vr is corrosion reaction and Vm is mass transfer effect.

The corrosion reaction can be calculated using the following equation:

36

)(34.0)log(581.0273

11984.4log22 COactCOr pHpHf

TV

(2.41)

And the mass transfer variable is defined as:

22.0

8.0

8.2 COm fdUV (2.42)

Where; T is temperature (oC), fCO2 is fugacity CO2 (bar), pHact is pH actual, 2COpH is

the pH of pure water saturated with CO2 at prevailing temperature and pressure.

The fugacity of CO2 is similar to its partial pressure, but corrected for non-ideality

of CO2 at high pressure and temperature. The mass transfer represents the main part

of the dependence on flow velocity U and pipe diameter d.

Cassandra (DWM 93)

Cassandra [76] is developed based on the experiences of de Waard and Milliams

[8]. The input includes pH, CO2 concentration, temperature, and water contaminant.

This model does not consider scaling temperature. The user must set an assumption of

the scaling temperature. The basic formula to calculate corrosion rate is expressed as

in Equation 2.51 below:

)log(67.0/17108.5)log(2COr PTV (2.43)

This model can be used to calculate effects of corrosion inhibitor availability and

corrosion risk categories on corrosion rate. The model also accounts for the presence

of acetate in water as HAc.

The major input to the model are: CO2 mole %, temperature, total pressure, liquid

velocity and water chemistry. Besides that, the model has secondary input, such as

hydraulic diameter and glycol concentration, oil type (crude or condensate) and water

type (condensed water or formation water). The effect of oil wetting in this model is

37

not included. Semi empirical model is developed both based on best fit parameters

and theoretical background to understand physical parameters. Same with description

presented above, semi empirical model needs large experiments database used to

either model regression and to find fundamentals variables involved.

From the brief model description presented above, it is clear that for an improved

empirical, semi empirical and mechanistic model, a better understanding of both

design of experiment (DOE) and mechanistic of CO2 corrosion theory is crucially

needed. Using DOE, an optimum model improvement can be achieved efficiently.

The present research work will develop a CO2 corrosion model founded on

fundamental theory and systematic statistics approaches that expresses relationship

between the reservoir species (HAc, H2S) and operational conditions (temperature,

pH, flow condition).

2.5 Simulation of Flow Analyses

Flow-induced corrosion is a type of corrosion caused by a combination of mechanical

and electrochemical effects. Mechanical effects due to water motion causes

impingement that leads to metal removal and material abrasion. Water that flows to

the surface can wear the corrosion product film or create shear stress to the surface.

Corrosion rate also can increase due to effects of differences in velocity turbulence

across the surface. Parallel flow can also reduce thickness of the boundary layer, thus

allowing active species to reach the metal surface quickly. Parameters that influence

flow induced corrosion are hydrodynamic boundary layer and rate of momentum

transfer from the bulk to the wall. In this condition, corrosion may be controlled by

the rate of mass transfer of a reactant or the rate of corrosion products [36].

2.5.1 The uses of rotating cylinder electrode to simulate flow induced corrosion

Rotating Cylinder Electrode (RCE) has been widely used to simulate flow in the

pipeline. RCE is an alternative corrosion test that can be used to simplify flow

induced corrosion phenomena from flow loop system [35]. Laboratory flow loop

38

system requires complex arrangements and is expensive to maintain. RCE is a simple

equipment that can be used to study corrosion process under velocity and turbulent

conditions. By using RCE, fluid flow effects on corrosion can be simulated in the

laboratory and it is possible to control the hydrodynamic conditions that occurs on the

surface of the metal sample.

2.5.2 Turbulent and mass transport in RCE experiments

At high rotation flow, the solution flow will have complex mechanism creating

several model flows [32]. The shear stress on the sample surface becomes significant

to form turbulent flow. The transition from laminar flow to turbulent flow can be

related to Reynold’s number as in the following equation [38]:

vulRe (2.44)

v (2.45)

Where ρ is the solution density (g cm–3), and µ is the absolute viscosity of the solution

(g cm–1s–1).

The linear velocity, Ucyl (cms–1), at the outer surface of the cylinder is given by Ucyl =

ω rcyl = π dcyl f /2

Where the rate can be expressed either as angular rotation rate, ω (rad s–1), or as f

(rpm). In general, turbulent flow will be achieved by rotating cylinder when the

Reynold’s number is greater than 200 or 20 rpm.

This turbulent flow creates a concentrated solution near the metal surface from the

bulk solution, thus a concentration gradient is formed. This condition can be a factor

that governs corrosion behavior as an effect of oxygen transport. Corrosion reaction

occurs at the solution through diffusion mechanism. Thus the current can be limited

by rate of diffusion reactions. The diffusion limited current density is given by:

39

dxdcFDi (2.46)

Where dxdc is concentration gradient.

For the maximum of concentration gradient, the diffusion limited current

density can be written as:

0

limxbulk cc

FDi (2.47)

Where: iL is limiting current for anodic reaction, Cbulk is bulk concentration of

cathodic current, is diffusion layer thickness, D is coefficient of diffusion and F is

Faraday’s constant.

As reported by Eisenberg [77] the most commonly accepted description for RCE

mass transport, particularly, the mass transfer coefficient, Km (cms–1) to a rotating

cylinder is given by the following relationship:

Km = (D / dcyl) Sh

= (D / dcyl) (0.0791 Re0.7 Sc

0.356) (2.48)

Where the diffusivity, D (cm2s–1), is usually taken as the diffusion coefficient for

the molecule or ion undergoing mass transport, and Sh and Re are the dimensionless

Sherwood’s and Reynold’s numbers, respectively. The Schmidt number, Sc = μ / (ρ

D), is also a dimensionless number. The overall mass transfer coefficient to an RCE

can be expressed in one of three forms [37]:

Km = 0.0791 dcyl –0.3 (μ / ρ) –0.344 D+0.644 Ucyl+0.7 (2.49)

40

In general, the mass transport limited current density, jlim (A cm–2), observed in an

electrochemical experiment is related to the mass transfer coefficient by the following

relationship,

Jlim = ilim / A = z F C Km (2.50)

Combining Equation 2.49 and Equation 2.50, the mass transport limited current

density can be expressed as follows:

jlim = 0.0791 z F C dcyl –0.3 (µ/ρ)–0.344 D0.644 Ucyl 0.7 (2.51)

= 0.0487 z F C dcyl +0.4 (µ/ρ)–0.344 D0.644 ω 0.7

Where F is Faraday’s Constant (96484.6 C / mol), ilim (Ampere) is the limiting

current, and A (cm2) is the area of the electrode. To make full quantitative use of this

relationship, both the number of electrons exchanged, z, and the bulk concentration, C

of the ion or molecule involved in the electrochemical process must be known.

2.5.3 Wall shear stress for RCE

Shear stress is a stress, which is either parallel or tangential to the surface of a

material. The physical quantity of shear stress is measured in force divided by area. In

fluid flow, fluid moving along a surface will cause a shear stress on that surface. In a

no-slip condition, the fluid will have zero velocity relative to the boundary. The fluid

velocity at all liquid–solid boundaries is equal to that of the solid boundary. The speed

of the fluid at the boundary (relative to the boundary) is 0, but at some height from the

boundary the flow speed must equal that of the fluid. The region between these two

points is named the boundary layer. The shear stress can be expressed as [36]:

0

yw Y

U (2.52)

Where µ is the dynamic viscosity of the fluid, U is the velocity of the fluid along

the boundary and Y is the height of the boundary. The turbulent flow at the RCE

41

induces a wall shear stress on the surface of the cylinder. Again, Eisenberg reported a

well-accepted equation for the wall stress, τcyl (g cm–1 s–2):

τcyl = 0.0791 ρ Re–0.3 Ucyl

2 (2.53)

Where τcyl is wall stress, ρ is density, Re is Reynold’s number and Ucyl is

velocity. There are relationships between rotation speed and wall shear stress for RCE

are calculated and tabulated in Table 2.1.

Table 2.1 Hydrodynamic Computations for a Typical Rotating Cylinder Electrode in

Water [78]

N (rpm)

ω (rad / sec)

Ucyl (cm / sec)

τcyl (g cm–1 s–2)

Re (unitless)

5 0.524 0.31 0.0025 42 10 1.047 0.62 0.0082 84 20 2.094 1.26 0.0267 169 50 5.236 3.14 0.1270 422

100 10.47 6.28 0.4125 844 200 20.94 12.6 1.3402 1688 500 52.36 31.4 6.3631 4219 1000 104.7 62.8 20.674 8438 2000 209.4 125.7 67.169 16876

These quantities assume a typical RCE tip with outer diameter 1.2 cm rotating in water at 25ºC. For pure water at 25ºC, the density is 0.997 g cm–3 and the absolute viscosity is 0.00891 g cm–1 s–1.

2.6 Design of Experiment (DOE) and Statistical Modeling

Empirical models have been used to predict corrosion process involving several

independent variables. However, most of the empirical models do not predict the

corrosion rate in the presence of several variables simultaneously [61]. Generally,

corrosion experimental data are limited by determination of dependent factors. Most

researchers use selected dependent variables based on specific interval variables

which have not been well verified (planned interval test). This is a simple method and

believed to represent overall unselected variables, but, this method lacks statistical

analysis that supports the conclusion.

42

In fact, there have been many theoretical papers on statistical analyses with

response surface methodology technique published the last decade [79-82]. Although

those papers have discussed response surface design in the research, there are not

many applications of response surface methodology in corrosion processes were

published, especially corrosion in CO2 system and CO2/H2S/HAc system. There was

one paper registered for NACE conference in 2009 [68] discussed corrosion

mechanism of mild steel in the presence of CO2, O2 and inhibitor. However, the paper

did not consider for other various conditions, especially corrosion that occurs in the

presence of HAc and H2S. In order to identify the key mechanism influencing CO2

corrosion simultaneously, the effects of main parameters such as HAc, temperature,

pH, and flow are still under investigation and need more widely reviewed by

researchers.

2.6.1 Design of experiments (DOE) and response surface methodology (RSM)

The application of response surface methodology (RSM) allows a visualization of the

experimental results in a 3-D display [83]. RSM is used to determine optimal levels

for variables input. RSM is a sequential procedure for constructing empirical relation

for the experimental data. Using response information, the optimum data between

factors can be developed and model improvements can be achieved. It has been

proven that researchers have used response surface method (RSM) to process data

systematically that can allow to apply multiple regression simultaneously[68, 84].

Response surface design methodology is also often used to refine models to obtain an

optimum design. Using RSM, the following advantages can be obtained [84].

Displays region of an experimental result in the form of response surface.

Response surface obtains the equation models that inform changes in input

variables, which influence a response of interest.

Selects the operating conditions to meet specifications.

43

2.6.2 Types of response surface designs

There are several types of response surface design in literature. Generally, each model

is developed based on the number of experiments and the number of design variations

that can be constructed. The following are four types of RSM design.

CCD

CCD is appropriate for incorporating the full quadratic models. CCD consists of a

factorial design (the corners of a cube) together with center and axial points that allow

for estimation of second-order effects. For a full quadratic model with n factors, CCD

sets (2n + 2n + 1) minimum number of experimental running for estimating and (n +

2)(n + 1)/2 for number of coefficients [81]. The central CCD comprises 2n factorial

points taken from a full factorial at levels ± 1, 2n axial points at locations ± α, and nC

the center point of origin. Figure 2.1 illustrates a CCD for three variables. Box and

Hunter [83] have discussed and calculated the values for α and central point needed to

run the experiments.

Figure 2.1 Location of experiments running in CCD for 3 variables [83].

Box-Behnken design

Box-Behnken design (BBD) [83] typically has fewer design points, therefore it has

less experiments to run. BBD is an appropriate design to estimate the first-order

coefficients. In estimating second model regression, Box-Behnken designs are not

recommended. Box-Behnken designs are rotatable and suitable for a small number of

factors that require fewer runs than CCD. By avoiding the corners of the design space,

BBD will reduce experimental cost compared to CCD.

44

Factorial Experiments

Full factorial designs measure response variables using every treatment (combination

of the factor levels). A full factorial design for n factors with N1, ..., Nn levels requires

N1 × ... × Nn experimental runs for each treatment. Fractional factorial designs use a

fraction of the runs required by full factorial designs. Factorial design is selected

based on an assumption of which factors and interactions have the most significant

effects. The factorial experiment does not have center points and no replicates.

Therefore, there are only limited experimental runs [83].

Plackett-Burman Designs

Plackett-Burman designs are used when only the main effects are considered

significant. Two-level Plackett-Burman designs require less number of experimental

runs.

2.6.3 Determination of the stationary conditions

RSM is useful to obtain critical points in the experimental variables. The surfaces

generated by linear or polynomial models will be used to indicate the direction in

which the original design must be started to attain the optimal conditions. For

polynomial models, the critical point can be characterized as maximum, minimum, or

saddle. Using RSM, it is possible to calculate the coordinates of the critical point

through the first derivative of the mathematical function. First derivative equals to

zero indicates that critical points is located.

2.6.4 Model estimation

Model estimation is a type of model used to predict trend of data [84]. The model

order is an important factor in making model regression that relates independent

variables. There are common fitting regression model that can be used to predict

trend.

Linear : Y = B0 + B1X1 + B2X2 + . . . .. BkXk (2.54)

Power : Y = B0(X1B1)(X2

B2) ………. .. (XkBk) (2.55)

45

Exponential : Y = B0(B1X1)(B2

X2) ……….. (BkXk) (2.56)

Linear model estimation

The response is modeled as linear combination functions of the predictor, plus a

random error ε. The expressions fj(x) (j = 1, ..., p) are the terms of the model. The βj (j

= 1, ..., p) are the coefficients. The errors, ε are assumed to be uncorrelated and

distributed with mean 0 and constant variance.

The estimated linear model is given by:

Y = b0 + b1X1 + b2X2 + . . . bkXk. (2.57)

Where, Y = response or independent variable, b = coefficient variables and x =

dependent variables.

Multiple linear regression

If the predictor x is multi dimensional, the functions fj that form the terms of the

model, consist of several functions. The model might include f1(x) = x1 (a linear term),

f2(x) = x12 (a quadratic term), and f3(x) = x1x2 (interaction term). Response variable y

is modeled as a combination of constant, linear, interaction, and quadratic terms

formed from two predictor variables x1 and x2. Uncontrolled factors and experimental

errors are modeled by ε. Given the data for x1, x2, and y, regression estimates the

model parameters βj (j = 1, ., n).

There is a curvature of general second order model which is expressed as [83]:

ji

jiij

k

i

k

iiiiii XXXXY

1 1

20 (2.58)

Where Y = response that can fit the following linear, quadratic, or cubic regression

models, β = regression constant, Xi and Xj = main effect of dependence factors, and

XiXj = interaction effects between dependence factors.

46

Power and exponential model regression

To estimate the power model, ln(Y) is regressed on ln(X1), ln(X2), . . . , ln(Xk).

Coefficients for the original predictor variables are b0 = exp(b0') and bi = bi', for i = 1,

. . . , k. The estimated power regression model is given by:

Y = b0(X1b1)(X2

b2) . . . (Xkbk). (2.59)

Exponential model regression can be estimated using ln(Y) regressed on X1,X2, . . Xk.

Coefficients for the original predictor variables are:

bi = exp(bi') , i = 0, . . . , k. The estimated exponential model is:

Y = b0(b1X1)(b2

X2) . . . (bkXk). (2.60)

2.6.5 Calculation of regression coefficients

In experiments, there are observed variables called responses, and variables that can

be adjusted called predictors. Those two parameters can be entered to the data

matrices as [83]:

Predictors : Xnx(k+1) = [ 1 Xn1 Xn2 . . . Xnk ]

[ 1 X11 X12 . . . X1k ]

[ 1 X21 X22 . . . X2k ]

Response : Yx1 = [ Y1, Y2, …… ., Yn ]

Unit vector : Ux1 = [ 1, 1, . . . ….……, 1 ]

The estimated regression coefficient (b) for the model is calculated using the least

squares method to fit the regression model, and is given by the equation:

b = [XT.X]-1.XTY (2.61)

Then,

ŷ = Xb (2.62)

e = Y – ŷ (2.63)

47

2.6.6 Model accuracy measurement

2.6.6.1 Model adequacy

To check how accurately the model describes the data and predicts a response, there

are common parameters that can be used to observe the data. To check model

performance, the following model assumptions should be met [83]:

Linearity – The true relationship between the mean of the response variable e

(Y) and the explanatory variables x1, …, xk is a straight line.

The random errors, εi, are independent, identically distributed random

variables with distributions.

The assumption of the linearity and random error are analyzed using [83]:

Normality Assumption

The normality plot for assessing data set is approximately normally

distributed. Normality plot shows a normal distribution centered at zero for the

normality assumption.

Residuals vs. Time Sequence

The plot of residuals vs. time sequence is used to determine residuals

correlation or dependency of residuals in time sequence. A positive correlation

is represented by runs of positive and negative residuals which are translated

as independent assumptions on the errors.

Residuals vs. Fitted Values

The better model, plot of residuals versus fitted values should exhibit no

particular structure. A plot with no obvious pattern indicates residuals are

unrelated to any other variables.

Residual plots

It is used to examine the goodness of a model fit in regression and ANOVA.

Examining residual plots to determine the least squares assumptions are being

met.

48

2.6.6.2 Model validation

Model validation of empirical model equation is used to evaluate experimental data

which referred to proven data. The accuracy and precision of the model is represented

as [83]:

Residual

The residual sum of squares is the variation attributed to the error. The larger this

value is, the better the relationship explaining data.

Residual (e) is defined by:

e = y -

y (2.64)

Coefficient determination

Coefficient determination (R2)is defined as [83]:

_

_

2

ii

i

total

reg

yy

yy

ssss

R (2.65)

Where yi = observed response,

iy predicted response value, _

iy mean response

and SSreg = sum of square of regression, SStotal = sum of square of total.

In matrix form, scalars SSreg and SStotal are calculated and used to obtain the

coefficient of determination R2 (goodness-of-fit), sum square of error (SSe) and Fstat

(statistical significance) as follows [83]:

SSreg = bTXTY - (1/n)(YTUUTY) (2.66)

SSe = YTY – bTXTY (2.67)

SStotal = YTYT - (1/n)(YTUUTY) (2.68)

R2 = SSr/SStotal (2.69)

Fstat = (SSr/k)/(SSe/(n-k-1)) (2.70)

P-value

49

It determines the appropriateness of rejecting the null hypothesis in a hypothesis test.

P-values range from 0 to 1. A commonly used p-value is 0.05. If the p-value of a

statistical testis less than the setting (α), the null hypothesis is rejected. A null

hypothesis is when there is no effect of the variables to the response [83].

Fstat

It is a hypothesis test that examines the ratio of two variances to determine their

equality that can evaluate distribution of data. If the observed F-statistic exceeds the

critical value, the null hypothesis is rejected. That other equation is more commonly

shown in an equivalent form [83]:

22

2121

/)/()(

DFSSDFDFSSSSFstat

(2.71)

Where, SSi = Sum of square of variable i and DFi = Degree of freedom of

variable i.

Correlation

The correlation coefficient allows researchers to determine if there is a possible linear

relationship between two variables measured on the same subject [83].

22

yyxx

yyxxS xy

(2.72)

Where Sxy is correlation, y and x are the response prediction and experimental

results respectively. While

y and

x are response prediction and average experimental

results sample mean respectively.

Standard error

The standard error for the predicted response is calculated by:

50

i

ii

yyy

errorSt

. (2.73)

The variable St.error is a standard error of the response while yi and ŷ are the

response variable and response variable predicted respectively.

In order to develop a model that considers effects of species and operation conditions

on corrosion rate simultaneously, it is important to select a statistical methodology

that can be applied in CO2 corrosion. In this research, a statistical technique of RSM

is proposed for the construction of an empirical model that relates effects of HAc,

temperature, and rotation speed on CO2 and H2S environments. The RSM offers the

best alternative to study the corrosion rate of carbon steel in CO2 environments. In

addition to, RSM can also be combined with mechanistic theories to analyze

experimental data efficiently. Once the data were collected, the data were generalized

using least sum square method to estimate the parameters in regression model. Then,

the model was validated and verified with proven data to quantify the performance of

the model.

51

CHAPTER 3

RESEARCH METHODOLOGY

The research methodology can be divided to the three main steps; modeling design of

the experiment, experimental work, and model development and evaluation. The first

step was conducted by screening suitable design experiment and identifying historical

data variables to find the trending of the CO2 corrosion model. Historical data was

provided by CO2 corrosion database and calculation from mechanistic theory. Once

CO2 corrosion trending was found, the best type of experiment design and the model

regression can be selected. The next step involved the experimental work based on

design of experiment to develop the model. In order to evaluate the model

performance, the model was verified with published experimental data and corrosion

software calculation. The model performance was stated by the value of standard

error estimation, coefficient determination and correlation that represents the accuracy

and precision of the model compared to the data provided. The steps are summarized

in Figure 3.1.

52

Figure 3.1 Flow chart of the research methodology.

Expe

rimen

tal

wor

k

T : Temperature

N : Rotation speed

HAc : Acetic acid

concentration

53

3.1 Design of Experiment

Design of experiment (DOE) is used to plan experiment in order to obtain the results

that can be analyzed analytically and proven statistically. Thus, the individual and

interaction effects from the experiment can be analyzed simultaneously. Using design

of experiment allows controlling the independent and dependent variables to meet the

statistical criteria. This experiment used central composite design (CCD) to model the

CO2 corrosion model. CCD is designed to build a second order (quadratic) model for

the response variable without performing full randomized variables in the experiment.

In other cases, full factorial design (FFD) was applied in the calculation by combining

the experimental data conducted in condition at pH 4 and pH 5.5. A full factorial

experiment is an experiment whose design consists of two levels which can be applied

to predict effect of pH as independent variables. The pH values used to study

corrosion rate are similar to many field operation conditions [1,2].

3.1.1 Selection of Experimental Factors

Before designing the experiments that will be used for the corrosion RSM model, the

corrosion problem and available design experiment must be identified. This stage is

conducted by screening the variables values that will be used in design experiments in

order to obtain a RSM model that can represent the behavior of output response. The

RSM model output will be analyzed using DOE. In this research, CCD and FFD were

selected to study CO2 corrosion. CCD was used to construct a CO2 corrosion model

with temperature, HAc and rotation speed as independents variables. While, FFD was

to construct model which involving pH as an additional independents variables

including temperature, HAc and rotation speed.

The first step to construct the RSM model is to determine a possible model trend.

Initially, corrosion model trends were identified in correlation with the selected

factors mechanistically. This was performed by studying the history of the corrosion

data and examining their behavior from corrosion mechanistic theories. The corrosion

model can be developed when the factors affecting CO2 corrosion are known. The

factors tested are presented in Table 3.1.

54

Table 3.1 Experimental Parameters

Purged gas CO2, N2, CO2/H2S (300 ppm H2S)

Total pressure Atmospheric

HAc concentration 0 to 340 ppm

Temperature 22 to 80°C

Rotation rate (N) 0 rpm to 6000 rpm

pH 4.0 and 5.5

Measurement techniques Potentiodynamic sweeps (PS),

Linear polarization resistance (LPR),

Electrochemical impedance spectroscopy (EIS)

The experimental variables values selected in the experiments were based on

considerations that those values are similar to which found in many field production

conditions. It was recorded that the natural gas produced in many other locations

around the world have H2S content in the range of 0 -1000 ppm and HAc

concentration that reaches 800 ppm [1-5]. While operating conditions such as

temperature is from 22 to 120oC [4]. Many researchers have studied effects of those

species variables on corrosion rate, so data provided by previous researchers can be

used for additional corrosion information and for model evaluating to show the

methodology performances which used in this experiments.

3.1.2 Variable coding and experimental design

A CCD, with three variables, was used to study the response pattern and to

determine the combined effect of variables. The effect of the independent variables of

HAc concentration, temperature and rotation speed in CO2 environments are shown in

Table 3.2. Table 3.3 was used to study effects of HAc, Temperature and rotation

speed in CO2/H2S environments. In order to make variables in the experiments vary in

the same range, the value of variables should be in coding value. This code value is

also important in controlling the result to meet a normal distribution pattern [85]. The

variables were coded according to the following equation [85].

55

1)()(2

lowhigh

highcode XX

XXx (3.1)

Where

xi = dimensionless value of an independent variable

Xi = real value of an independent variable

Table 3. 2 Natural and coded independent variables used in RSM to study corrosion

rate in CO2 system.

Level Code HAc

(ppm)

T

(oC)

N

(rpm)

pH

Axial point 3 340 80 6000 -

High 1 270 70 4000 5.5

Centre 0 170 50 2000 5

Low -1 70 35 1000 4

Axial point -3 0 22 500 -

Table 3.3 Natural and coded independent variables used in RSM to study for CO2/H2S

system.

Level Code T

(oC)

HAc

(ppm)

N

(rpm)

Axial point 3 80 136 6000

High 1 70 108 4000

Centre 0 50 68 2000

Low -1 35 28 1000

Axial point -3 22 0 500

3.1.3 Setting up experimental design

The technique used to calculate independent variables simultaneously and to estimate

model regression of CO2 corrosion was response surface methodology. In this

method, the independent variables are calculated based on matrices operations to find

56

regression equations. The following Table 3.4 was an experimental matrix designed

using RSM method to obtain CO2 corrosion equations at pH 4 and pH 5.5.

Table 3.4 CCD experimental design matrix with three variables (coded and natural)

used to study the response pattern and to determine the effects of combined variables

Coded variables Natural variables

Experimental

points

No.

of

run

HAc

T

N HAc

(ppm)

T

(oC)

N

(rpm)

1 1 1 1 270 70 4000

2 -1 1 1 70 70 4000

3 1 -1 1 270 35 4000

4 -1 -1 1 70 35 4000

5 1 1 -1 270 70 1000

6 -1 1 -1 70 70 1000

7 1 -1 -1 270 35 1000

Factorial points

8 -1 -1 -1 70 35 1000

9 3 0 0 340 50 2000

10 -3 0 0 0 50 2000

11 0 3 0 170 80 2000

12 0 -3 0 170 22 2000

13 0 0 3 170 50 6000

Axial points

14 0 0 -3 170 50 500

15 0 0 0 170 50 2000

16 0 0 0 170 50 2000

17 0 0 0 170 50 2000

Centre points

18 0 0 0 170 50 2000

Table 3.5 shows a FFD design where the experimental matrix arrangement where data

were taken from the factorial design within CCD matrix at pH 4 and pH 5.5. As can

be seen from the Table 3.4 and Table 3.6, that, in CCD, the experiments consist of 8

57

runs as a factorial, 6 runs as a axial points that used to extend the model regression,

and 4 runs as a repetition to evaluate repetitions of the experiment.

Table 3.5 Factorial experimental design matrix with four variables (coded and

natural) used to study the effect of pH on CO2 corrosion.

Coded variables Natural variables No. of

run

pH T HAc N pH

T

(oC)

HAc

(ppm)

N

(rpm)

1 -1 -1 -1 -1 4 22 0 1000

2 1 -1 -1 -1 5.5 22 0 1000

3 -1 1 -1 -1 4 60 0 1000

4 1 1 -1 -1 5.5 60 0 1000

5 -1 -1 1 -1 4 22 60 1000

6 1 -1 1 -1 5.5 22 60 1000

7 -1 1 1 -1 4 60 60 1000

8 1 1 1 -1 5.5 60 60 1000

9 -1 -1 -1 1 4 22 0 6000

10 1 -1 -1 1 5.5 22 0 6000

11 -1 1 -1 1 4 60 0 6000

12 1 1 -1 1 5.5 60 0 6000

13 -1 -1 1 1 4 22 60 6000

14 1 -1 1 1 5.5 22 60 6000

15 -1 1 1 1 4 60 60 6000

16 1 1 1 1 5.5 60 60 6000

17 -1 0 0 0 4 35 40 3000

18 1 0 0 0 5.5 35 40 3000

19 0 -1 0 0 5 22 40 3000

20 0 1 0 0 5 60 40 3000

21 0 0 -1 0 5 35 0 3000

22 0 0 1 0 5 35 60 3000

23 0 0 0 -1 5 35 40 1000

24 0 0 0 1 5 35 40 6000

58

Table 3.6 CCD experimental design matrix with three variables (coded and natural)

used to study corrosion in CO2/H2S system.

Coded variables Natural variables

Experimental

points

No

of

run

HAc T N

HAc

(ppm)

T

(oC)

N

(rpm)

1 1 1 1 108 70 4000

2 -1 1 1 28 70 4000

3 1 -1 1 108 35 4000

4 -1 -1 1 28 35 4000

5 1 1 -1 108 70 1000

6 -1 1 -1 28 70 1000

7 1 -1 -1 108 35 1000

Factorial

points

8 -1 -1 -1 28 35 1000

9 1.7 0 0 136 50 2000

10 -1.7 0 0 0 50 2000

11 0 1.7 0 68 80 2000

12 0 -1.7 0 68 22 2000

13 0 0 1.7 68 50 6000

Axial points

14 0 0 -1.7 68 50 500

15 0 0 0 68 50 2000

Centre points 16 0 0 0 68 50 2000

3.1.4 Parameters estimation

The constants of parameters estimations were used to determine empirical relationship

in regressions equations. Data from the CCD matrices (Table 3.4 – 3.6) were analyzed

using the least sum squares method to fit the second–order polynomial. The second

order model selected was based on CO2 corrosion mechanistic theories developed by

George et.al [86]. Constants parameters model was calculated using Equation 2.68

(second order model) to obtain the regression model that represents an empirical

relationship between the tested variables.

59

3.1.5 Model accuracy measurement

Model accuracy is a technique that can be used to check the appropriateness of the

regression model. It can be divided into model adequacy and model validation [83].

Model Adequacy is used to evaluate how accurate the model describes the data

and meet the statistical criteria.

Model Validation is an indicator how well the regression model fit the observed

data.

3.2 Corrosion Experiments

The experiments were performed both in stagnant (static test) and flow simulation

condition (dynamic test) with using rotating cylinder electrode (RCE) as simulation of

flow in pipeline. The electrochemical technique measurements used in this

experiment were linear polarization resistance (LPR) and electro chemical impedance

spectroscopy (EIS) were used to measure the corrosion rate. The procedure is similar

to ASTM Experimental test G 5-94 [87].

3.2.1 Specimen preparation

The working electrodes were carbon steel with chemical composition shown in Table

3.7. The cylindrical specimens have a diameter of 12 mm and length of 10 mm.

Before immersion, the specimen surfaces were polished successively with 150, 240,

400 and 600 grit SiC paper, rinsed with methanol and degreased using acetone as

referred from reference [61]. The experiments were repeated at least twice in order to

ensure reasonable reproducibility.

60

Table 3.7 Composition of 080A15 (BS 970) carbon steel used in the experiments.

Steel C

(%)

Si

(%)

Mn

(%)

P

(%)

S

(%)

Cr

(%)

Ni

(%)

Fe (%)

080A15 0.15 0.18 0.799 0.01 0.03 0.06 0.065 Balance

3.2.2 Static test

In static test, corrosion behavior was studied in stagnant condition where there was no

flow rate occurring in the solution. A typical experimental arrangement for the static

test is illustrated in Figure 3.2. The test assembly consists of one liter glass cell

bubbled with CO2. The required test temperature was set at the hot plate. The

electrochemical measurements were based on a three-electrode system, using a

commercially available potentiostat with a computer control system. The reference

electrode used was Ag/AgCl and the auxiliary electrode was a platinum electrode.

Legend: 1-Glass cell, 2-Reference electrode, 3-Counter electrode, 4-

Working electrode, 5-CO2 gas bubbler.

Figure 3.2 Experimental set-up for static test.

1

2

3 4 5

Potentiostat

Mixing tube

Flow meter

61

3.2.3 Dynamic experiments

Dynamic experiments were conducted in a one liter glass cell with polypropylene cell

lids. A three-electrode arrangement was used. The RCE, used to simulate flow

condition used in this research was made by PINE Research Instruments (Model

AFMSRCE) with rotation speeds from 0 to 10,000 rpm. The set-up is shown as in

Figure 3.3 below. A cylindrical working electrode was screwed to an electrode holder

at the center of the cell for rotation in the RCE. The Linear Polarization Resistance

(LPR) technique was used to measure the corrosion rate. The procedure is similar to

ASTM G 5-94 [87].

6

Legend :

1- Rotator

2- Counter electrode

3- Reference electrode

4- Gas bubbler

5-Working electrode

6-Potentiostat

Figure 3.3 Experimental set-up for RCE test.

The shaft and the specimen holder of the RCE were made of stainless steel. The

cylindrical sample was held in position with the use of PTFE holder and an end cap

screwed at the end of the specimen holder. The cylindrical samples used in the RCE

apparatus were machined from commercial carbon steel grade. The sample surface

was polished to 600-grade finishing using silicon carbide papers. The specimen was

degreased and rinsed with methanol and deionised water prior to immersion. A

schematic diagram of the specimen assembly, with dimensions of the samples, is

shown in Figure 3.4.

1 2 3 4 5

62

RCE Shaft (316 SS)

RCE Shaft Insulator(PTFE)

Test Coupon(Mild Steel)

End CapRubber Washer

Figure 3.4 Details of the RCE specimen assembly with electrode diameter of 12 mm

and length 8 mm.

3.2.4 Cell solutions

The total pressure was 1 bar, the glass cell was filled with 1 liter of deionized water

with 3% wt NaCl, which was stirred with a magnetic stirrer. Then, CO2 or

CO2/H2S/N2 gas was bubbled through the cell at least one hour prior to the

experiments, in order to saturate and de-aerate the solution. Temperature was set

using a hot plate. After the solution has been prepared, the pH was adjusted to the

required pH using NaHCO3 as a buffer solution. During the experiment, constant flow

of gases at a fixed pressure was continuously bubbled through the electrolyte in order

to maintain consistent water chemistry.

3.2.5 Composition of gases

Experiments was conducted in CO2 gas and mixed CO2/H2S gas environment. In CO2

gas system, the experiments used saturation condition of CO2 gas where concentration

of CO2 gas depends on temperature as presented in Table 3.8. Experiments in

CO2/H2S system used gas mixtures comprising 0.3 % H2S/N2 obtained commercially

from MOX®. The mixture of H2S balanced with N2 and CO2 was adjusted using gas

regulator and flow meter purged to the glass cell through a mixing tube. N2 was used to

substitute for methane for safety reasons. N2 as an inert gas was also important to de-

aerated the solution and maintenance the pressure. The compositions of the mixed gases

are given in Table 3.9.

63

Table 3.8 Vapor pressure of water [61].

T (°C) Vapor pressure of water

(mm Hg)

CO2 (% mole)

25 24 97

40 55 93

60 149 76

Table 3.9 Composition of gases used in the experiment.

CO2

(bar)

H2S

(mbar)

N2

(bar)

H2S

(ppm)

CO2

(ppm)

CO2/H2S

(ratio)

0.7 0.3 0.2997 300 700000 2333

3.2.6 Preparation of solutions

The solutions were prepared using glacial HAc, NaAc, and sodium bicarbonate

(NaHCO3). All reagents were analytical grade chemicals. The 3% NaCl solution was

saturated with CO2 by purging for at least one hour prior to immerse the electrode in

the solution. The pH of the solution was adjusted by adding a known amount of 1M

NaHCO3. The pH of the solution was checked by a microcomputer controlled pH-

meter, METTLER-TOLEDO Model 320, which had been calibrated using standard

buffer solutions.

3.2.7 Addition of HAc and acetate

The amount of HAc/acetate added to the solution was determined by the Handerson-

Hasselbach equation in order to maintain the required pH.

Handerson-Hasselbach equation: (pH = pKa + log10 [Base]/[Acid])

For acetic buffer, this is given by:

64

pH = 4.76 + log10[CH3COO-]/[ CH3COOH] (3.2)

The ratio of acetate ions and HAc at each pH is shown in Table 3.10 below.

Table 3.10 Calculated ratio of base and acid.

Ratio of Concentration (M) pH Value

[CH3COO-] [CH3COOH]

4 1 5

5 2 1

5.5 5 1

6 17 1

The calculated concentration of the HAc species in solution are shown in Table

3.11. It is assumed that the concentration of the HAc species remained the same at

different temperatures since the equilibrium constant for HAc KHAc varies a little with

temperature.

Table 3.11 Concentration of HAc species (ppm) in NaCl-CO2 saturated solution.

pH 4 pH 5.5

Species 30

ppm

72

ppm

120

ppm

132

ppm

30

ppm

66

ppm

108

ppm

138

ppm

HAc 25 60 100 120 5 11 18 23

NaAc 5 12 20 12 25 55 90 115

3.2.8 Electrochemical measurement

The measurement used three types of electrodes (working electrode, reference

electrode and counter electrode) connected to potentiostat. The electrodes are

immersed in the electrolyte solution. Electrochemical technique records

electrochemical process during oxidation and reduction in corroding solution.

Electrochemical corrosion experiments measure current oxidation by controlling

potential of the samples (working electrode). The measured current is plotted against

potential in the Tafel plot where the slope of polarization resistance is determined.

65

This polarization resistance is assumed as corrosion resistance that can be used to

calculate corrosion rate as presented by Equation 3.4 – 3.5.

3.2.8.1 Linear polarisation resistance (LPR)

LPR technique was used to determine the corrosion rates. The potential was swept

from Ecorr to 10 mV at sweep rate 10 mV/minute. For calculation of the corrosion

rates, Tafel constants was assumed to be 25 mV [61].

Polarization resistance (Rp) can be used to measure corrosion rate. Polarization

reistance is resistance at the location very near to Ecorr. At this point, the current

versus voltage curve approximates a straight line. The Stern-Geary equation can be

obtained to calculate corrosion rate is presented below [61]:

)(303.2 cap

cacorr bbR

bbI (3.3)

0)(

)(

Ecorr

p iE

IBR (3.4)

).(303.2.

ca

ca

bbbbB (3.5)

Corr. rate = Icorr 3272 EW/A (3.6)

Where:

Corr. rate = Corrosion rate (mm/y)

Icorr = Corrosion current (amps)

Rp = resistance polarisation

EW = The equivalent weight in grams/equivalent

= Metal density (grams/cm3)

A = Sample area (cm2)

ba = Anodic tafel slope

bc = Cathodic tafel slope

66

3.2.8.2. Electrochemical Impedance Spectroscopy (EIS)

EIS is one of the electrochemical methods to measure corrosion rate. EIS measures

corrosion rate by applying an AC potential to an electrochemical cell and measuring

the current through the cell without significantly disturbing the properties of the

surface. EIS technique uses a small excitation signal ranging from 5 to 50 mV and the

range of frequencies from 0.001 Hz to 100,000 Hz. Moreover, EIS presents a

qualitative and quantitative analyses of surface characteristics. EIS also can give

information about the process occurring on the metal surface during corrosion and

further provides information of corrosion mechanisms on the surface.

3.3 Mechanistic Corrosion Model Prediction

A mechanistic model is a prediction model that uses fundamental theories. In

corrosion, mechanistic theories include electrochemical reactions and

thermodynamical processes occurring in the solution. The model also considers the

role of chemical reactions and physical changes involved during the corrosion

process such as standard state properties of species, thermodynamic model and

activities of both ionic and molecular species to develop the mechanistic model.

George et al. [86] has developed the mechanistic model for CO2 corrosion as

presented below (Equation 3.7 – 3.9). The model has been verified with many

experimental data which showed reasonable results.

(i) Convective diffusion reactions through the mass transfer boundary layer. iobiimi cckFlux ,,

(3.7)

(ii) Molecular diffusion through the liquid in the porous outer scale:

ioioc

ii ccDFlux

(3.8)

(iii) Transfer ions through film by solid state diffusion can be formulated as:

is

iiRTB

ii cc

eAFlux K

,

,ln (3.9)

67

3.3.1 CO2 Corrosion in film free formation condition

The CO2 corrosion mechanism involves electrochemical reaction and diffusion

process that can be expressed mathematically. In these theories, the electron transfer

is assumed as a corrosion rate. The electron transfer that passes through the film based

on mechanistic theory provided by Nesic et al. [86] is expressed as:

is

imi

ociib

RTB

ii ckD

CRceACR K

,

,,

1

ln

(3.10)

Specific formula to calculate corrosion mechanism caused by CO2 gas is

formulated as follows [86]:

3232

2

502

222

2

1

ln

COH.

hydf

hydCOH

CO

mCOco

ocCOb

RTB

iCO

fKkDCR

kDCRc

eACRCO

K

(3.11)

Where,

Km = mass transfer coefficient of species i (m/s),

,bc = bulk concentration of species i (mol/m3),

oc = the interfacial concentration of species i at outer scale/solution interface

(mol/m3),

iD = diffusion coefficient for dissolved species i (m2/s),

= outer scale porosity,

= tortuosity factor,

ic = interfacial concentration of species I,

os = the thickness of outer film scale,

hbl = the thickness of turbulence boundary layer,

68

mbl = the thickness of mass transfer boundary layer,

f = film thickness,

A = Arrhenius constant ,

Tk = temperature (Kelvin),

cs = surface concentration,

R = universal gas constant.

3.4 Corrosion Predictions

There are corrosion model prediction software developed by industries namely ECE

[75], Norsok [72], and Freecorp [88]. Those models calculate corrosion rate based on

the experiences of the software designer and from experimental data. In this research,

those models are used to validate experimental data and to evaluate the model

performances.

This studies were conducted in order to formulate empirical corrosion prediction

models based on RSM technique. The experiments were performed under conditions

of varying temperature, rotation speed, and HAc concentration using LPR technique

in CO2 and CO2/H2S environments. The corrosion rate data were structured in the

matrices forms to find the model generation of empirical relationship among the

variables tested.

The corrosion rate data base from literature review and from software calculations are

required to quantify the RSM models. Comparison with corrosion rate data base have

been conducted to evaluate the accuracy and precision in predicting corrosion rate.

The details of the results are provided in the following chapter.

69

CHAPTER 4

EFFECTS OF HAc ON CARBON STEEL CORROSION IN CO2 ENVIRONMENT

This chapter presents the results and discussions of the effect of HAc, temperature,

flow condition indicated by rotation speed on carbon steel corrosion in CO2

environment. The studies carried out in this work include: identifying initial of

trending corrosion model, conducting experiments works based on design experiment

selected, generating experimental data results to find empirical constant parameters

used in the RSM model equation and evaluating the empirical model prediction.

Empirical model and statistical analyses were calculated by Minitab program software

[89]. In order to find a trending of the CO2 corrosion as an effect of independent

variable, CO2 corrosion mechanistic theory was applied. Then, the trend model is

used to fit the experimental data to obtain parametric relationships for the empirical

model. To evaluate the accuracy and precision, the RSM model were compared

against literature data from published papers and corrosion model calculated by

commercial corrosion software.

4.1 Initial Identification of Corrosion Rate Model

Corrosion process can be constructed mathematically from mechanistic theory by

using fundamental concepts of electrochemical reactions. The mathematical formulas

describing corrosion process are formed based on several assumptions as described in

Chapter 2. The trends of corrosion rate calculated by mechanistic theories are

presented in Figure 4.1 to Figure 4.4. Based on the trends, the RSM corrosion models

was fit using a second order model regression.

70

0.055

0.06

0.065

0.07

0.075

0.08

22 32 42 52 62 72Temperature (oC)

Cor

rosi

on ra

te (m

m/y

)

Figure 4.1 Simulated corrosion rate as a function of temperature from 22oC to 72oC, 1

bar and static in CO2 environment without HAc.

Figure 4.1 presents the relationship between corrosion rate and temperature. From

the graph, it is observed that corrosion rate increases exponentially with increasing

temperature. This corrosion rate model is confirmed with other corrosion rate models

as described by reference [28, 88].

0.051

0.0515

0.052

0.0525

0.053

0.0535

5 25 45 65 85 105 125HAc Concentration (ppm)

Cor

rosi

on ra

te (m

m/y

)

Figure 4.2 Simulated corrosion rate as a function of HAc concentration at 22oC, 1 bar

and static.

71

Figure 4.2 presents the mechanistic model for calculating the effect of increasing

HAc concentration on corrosion rate. From the figure, it can be observed that the

corrosion rate increases exponentially with HAc concentrations.

The effect of rotation speed on corrosion rate is presented in Figure 4.3. The

rotation speed is an important parameter to study the effect of flow conditions on

corrosion rate. Figure 4.3 shows that there exists a condition when flow rate do not

have significant impact on corrosion rate. As observed in Figure 4.3, the corrosion

rate becomes constant after a certain flow value even though the flow continues to

increase. Researchers define this condition as flow independent due to limiting current

density [61].

Figure 4.3 Simulated corrosion rate as a function of rotation speed for a range from

stagnant to 1000 rpm at 22oC and 1 bar.

4.2 Design of Experiment for Analyzing Corrosion Model at pH 4

The design selected for this experiment is a CCD with three independent variables.

This design is used to study corrosion rate and to determine the combined effect of

variables involved; temperature, HAc and rotation speed. It used a total of twenty

observations, consisting of eight observations as a factorial design, six observations as

axial points, and four points located in central points as repetitions.

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

0 200 400 600 800 1000Rotation speed (rpm)

72

Table 4.1 shows the effects of different concentration of HAc, temperature and

flow conditions (indicated by rotation speed) using LPR technique at pH 4. The test

was conducted for 1.5 hours and recorded the reading every 15 minutes. The

corrosion rate measurements are calculated based on the average corrosion rate during

1.5 hours measurements. More detail about the corrosion rate data against time are

presented in Appendix 1.

Table 4.1 CCD with observed values

for the response of experimental data (Yi).

Coded variables Natural variables No

HAc

(ppm)

T

(oC)

N

(rpm)

HAc

(ppm)

T

(oC)

N

(rpm)

Exp. results

(Yi)

1 1 1 1 270 70 4000 10.7

2 -1 1 1 70 70 4000 7.3

3 1 -1 1 270 35 4000 6.5

4 -1 -1 1 70 35 4000 4.4

5 1 1 -1 270 70 1000 10.7

6 -1 1 -1 70 70 1000 7.3

7 1 -1 -1 270 35 1000 6.4

8 -1 -1 -1 70 35 1000 4.2

9 3 0 0 340 50 2000 9.6

10 -3 0 0 0 50 2000 4.6

11 0 3 0 170 80 2000 9.5

12 0 -3 0 170 22 2000 3.8

13 0 0 3 170 50 6000 8.5

14 0 0 -3 170 50 0 7.3

15 0 0 0 170 50 2000 8.4

16 0 0 0 170 50 2000 8.5

17 0 0 0 170 50 2000 8.3

18 0 0 0 170 50 2000 8.2

73

4.2.1 Generalization of corrosion predictions model at pH 4, HAc

Data from the CCD matrix (Table 4.1) were fit by the second–order polynomial

(Equation 2.58) using the least sum squares method. A RSM constant parameter

model was calculated using Equation 2.61 and 2.62 which yielded the regression

Equation 4.1. The RSM regression model in Equation 4.1 represents an empirical

relationship between HAc concentration, temperature and rotation speed.

Y= -6.1170 + 0.0230(HAc) + 0.3160 (T) + 0.0005(N) -0.0001(HAc)2 -

0.0023(T)2 + 0.0002 (HAc× T) (4.1)

Where;

Y = corrosion rate (mm/y)

HAc = concentration of HAc (ppm)

T = temperature (oC)

N = rotation speed (rpm)

4.2.2 Prediction of CO2 corrosion model at pH 4

The average corrosion rate obtained from the experiments (Yi) is compared to data

from corrosion predictions (ŷ) as presented in Table 4.2. From the difference between

experimental results and RSM model predictions, it can be seen that there is a

reasonable results that indicates a satisfactory of the RSM model.

74

Table 4.2 Comparison between corrosion data experiments and corrosion data

predictions

Coded variables Natural variables No

of run HAc

T

N

HAc

(ppm)

T

(oC)

N

(rpm)

Exp. results

(Yi)

Predct.

(ŷ)

Error

(Yi-ŷ)

1 1 1 1 270 70 4000 10.7 10.7 -0.0

2 -1 1 1 70 70 4000 7.3 7.4 -0.1

3 1 -1 1 270 35 4000 6.5 6.8 -0.3

4 -1 -1 1 70 35 4000 4.4 4.7 -0.3

5 1 1 -1 270 70 1000 10.6 10.4 0.2

6 -1 1 -1 70 70 1000 7.2 7.0 0.2

7 1 -1 -1 270 35 1000 6.4 6.4 -0.0

8 -1 -1 -1 70 35 1000 4.2 4.2 -0.0

9 3 0 0 340 50 2000 9.6 9.1 0.5

10 -3 0 0 0 50 2000 4.6 4.5 0.1

11 0 3 0 170 80 2000 9.5 9.3 0.2

12 0 -3 0 170 22 2000 3.8 3.3 0.5

13 0 0 3 170 50 6000 8.5 8.1 0.4

14 0 0 -3 170 50 0 7.3 7.6 -0.3

15 0 0 0 170 50 2000 8.4 8.2 0.2

16 0 0 0 170 50 2000 8.5 8.2 0.3

17 0 0 0 170 50 2000 8.3 8.2 0.1

18 0 0 0 170 50 2000 8.2 8.2 -0.0

4.2.3 Variance Analysis

Table 4.3 shows the analysis of RSM regression model using variance analysis

calculated by CCD matrix according to Reference [84]. The main factors for the

coefficient of the linear and square models show a significant value at confidence

level of α = 0.05 (p<0.5). However, for the interaction effect of the model was

insignificant (p>0.5). Furthermore, the high values (98%) of the correlation

coefficients (R2) for the responses suggest that the RSM model has a good fit.

75

Table 4.3 Analysis of variance (ANOVA) for the fitted models.

Source DF Seq

SS

Adj

SS

Adj

MS F P

Regression 9 78.255 78.255 8.695 85.11 0.00

Linear 3 68.125 9.693 3.231 31.63 0.000

Square 3 9.368 9.364 3.122 30.55 0.000

Interaction 3 0.760 0.760 0.254 2.48 0.121

Residual

Error 10 1.021 1.021 0.102

Lack-of-Fit 5 1.001 1.002 0.201 50.77 0.000

Pure Error 5 0.019 0.019 0.0039

Total 19 79.276

R-Sq = 98.71%

4.2.4 Model adequacy evaluation

The performance of the RSM model was checked using normal plots of the residual.

As illustrated in Figure 4.4 to 4.6, it can be seen that all of the residual plots are in

good agreement with the model’s assumption of normal probability trend. The plot of

residual vs. probability percent, Figure 4.4, shows a straight line pattern. This

indicates that a normal distribution assumption has been satisfied and the coefficients

estimated with the minimum variance are unbiased. Figure 4.5, plot of residual vs.

order of data, is also identified as non-random error. This plot presents the assumption

that the residuals are uncorrelated with each other. Residual vs. fitted values plot,

Figure 4.6, shows a random pattern of residuals on both sides and no any recognizable

pattern in the residual plot. Thus, this model was in random distributions.

76

3210-1-2-3

99

95

90

80

70

60504030

20

10

5

1

Standardized Residual

Perc

ent

Figure 4.4 Normal plot of residuals.

16151413121110987654321

2

1

0

-1

-2

Observation Order

Stan

dard

ized

Res

idua

l

(response is C6)

Figure 4.5 Residuals versus order of data.

11109876543

2

1

0

-1

-2

Fitted Value

Sta

nda

rdiz

ed

Res

idu

al

Figure 4.6 Residuals versus Fitted Values.

77

In further analysis, each of the observed value for the corrosion rate was compared

with predicted values (Figure 4.7). Parity plot in Figure 4.7 shows a 98 % of

acceptable level of agreement. All of these results present a satisfactory mathematical

description of the corrosion rate data.

R2 = 0.99

0

2

4

6

8

10

12

0 2 4 6 8 10 12Predicted values (mm/y)

Obs

erve

d va

lues

(mm

/y)

Figure 4.7 The relationship between observed and predicted values of corrosion rate

model.

4.3 Verification with Experimental Data and Corrosion Prediction Software

The comparison of the resultant RSM model with Hedges’s [22] and George’s [86]

experimental data are shown in Figure 4.8 and Figure 4.9, respectively. A good

agreement between experimental and calculated data based on this corrosion

prediction RSM model is observed. Comparing to Hedges’s experiments at 60oC, the

RSM model has R2 of 94%, correlation of 97% and standard error estimation

deviation of 0.28 (± 0.22 mm/y). In comparison to George’s experimental data, the

RSM model shows a relationship with R2 of 93%, correlation of 97%, and standard

error estimation of 0.5 (± 0.4 mm/y). George’s experiment showed a good

relationship in correlation and regression relationship; but it provided less precision in

standard error estimation.

78

012

3456

78

0 20 40 60 80 100

HAc (ppm)

Cor

rosi

on ra

te (m

m/y

)

Exp. Model

Figure 4.8 Comparison between the model and Hedges’s experimental data

in 1 bar CO2, 60°C, and static condition.

0

1

2

3

4

5

6

7

8

22 27 32 37 42 47 52 57

Temperature (oC)

Cor

rosi

on ra

te (m

m/y

)

Exp. Model

Figure 4.9 Comparison between the RSM model and George’s electrochemical model

in 1 bar CO2, 100 ppm HAc, 300 rpm.

The comparison of the RSM model with corrosion prediction software Freecorp

[88] at 35oC is shown in Figure 4.10. The results show R2 of 90%, correlation of 94%

and standard error of 0.3 (± 0.2 mm/y). A good fit was also found when comparing

the RSM model with ECE [75] software as shown in Figure 4.11. The comparisons

79

show R2 of 90%, correlation of 97%, and standard error estimation of 0.5 (± 0.43

mm/y).

2

2.5

3

3.5

4

4.5

1000 2000 3000 4000 5000

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Free corp. Model

Figure 4.10 Comparison between the RSM model and Freecorp in 1 bar CO2, and

35°C.

0

1

2

3

4

5

6

30 40 50 60 70 80 90

Temperature (oC)

Cor

rosi

on ra

te (m

m/y

)

ECE Model

Figure 4.11 Comparison between the RSM model and ECE in 1 bar CO2, and static

condition.

The verification of the regression RSM model with this commercial software in a

different cases is presented in Appendix 2. The model has a good correlation with

80

average coefficient determination 90%, correlation 95% and standard error estimation

0.2 (± 0.15 mm/y).

4.4 Analysis and Interpretation of Response Surface of CO2 corrosion at pH 4

The RSM regression model can be graphically presented as response surface contour

to show the simultaneous effects of variables tested. The following figures 4.12 - 4.15

present simultaneous effects of temperature, HAc, and rotation speed on corrosion

rate at the pH 4 based on the RSM model. In further analyses, RSM model is also

used to calculate maximum corrosion rate caused by scaling temperature and limiting

current density indicated by critical values of the model.

4.4.1 Effects of temperature and HAc concentration

The effects of temperature and HAc concentration on the corrosion of carbon steel in

CO2 saturated solution is presented in Figure 4.12. The figure shows that an increase

in temperature and HAc concentration leads to an increase in corrosion rate. The

effects of HAc concentration on corrosion rate is smaller than the effects of

temperature within the range tested. In the range of temperature from 22 to 70oC, the

corrosion rate reached to 12.0 mm/y. In the range of HAc concentration from 0 to 340

ppm, the corrosion rate increased from 2.0 mm/y to 4.0 mm/y.

81

10

8

6

4

2

Temperature (deg. C)

HA

c (p

pm)

807060504030

300

250

200

150

100

50

0

Rot. speed (rpm) 0Hold Values

> – – – – – < 0

0 22 44 66 88 10

10

(mm/y)rateCorr.

ntour Plot of Corr. rate (mm/y) vs HAc (ppm), Temperature (

Temperature (deg. C) = 77.3206HAc (ppm) = 322.387Corr. rate (mm/y) = 10.5417

Figure 4.12 Response surface contours of corrosion rate as a function of temperature

and HAc concentration at pH 4 and stagnant condition.

4.4.2 Effects of temperature and rotation speed

The effects of temperature and rotation speed on the corrosion of carbon steel in CO2

environments, as modeled by RSM, is presented in Figure 4.13. In this conditions,

corrosion rate increases with increasing temperature and rotation speed. From the

figure, it can be seen effect of temperature has a greater effect than rotation speed.

Corrosion rate increased from 1 mm/y to 5 mm/y with increasing temperature from

25oC to 80oC. But, corrosion rate only increase from 1 mm/y to 2 mm/y with

increasing rotation speed from 1000 rpm to 6000 rpm. However, there was low

dependence of rotation speed on temperature. At the higher temperature (80oC),

corrosion was higher compared to lower temperature with increasing rotation speed.

For example, at 80oC, the corrosion rate was in the range of 4 mm/y to 5 mm/y. While

at the lower temperature (30oC), the corrosion rate was from 1 mm/y to 2 mm/y when

the rotation speed was increased from stagnant to 5000 rpm.

82

5

4

3

2

1

Temperature (deg. C)

Rot

atio

n sp

eed

(rpm

)

807060504030

6000

5000

4000

3000

2000

1000

0

HAc (ppm) 0Hold Values

> – – – – – < 0

0 11 22 33 44 5

5

(mm/y)rateCorr.

Temperature (deg. C) = 66.2537Rotation speed (rpm) = 3822.20Corr. rate (mm/y) = 5.37005

Figure 4.13 Response surface contours of corrosion rate as a function of temperature

and rotation speed at pH 4 without HAc.

4.4.3 Effects of rotation speed and HAc concentration

Figure 4.14 presents the surface response graph showing to the combined effect of

rotation speed and HAc concentration on the corrosion rate. The plot shows that

different corrosion rate is influenced by HAc concentration and rotation speed. At

higher HAc concentration (300 ppm), the corrosion rate increased from 3 to 3.5 mm/y

when the rotation speed was set from 0 to 3000 rpm. While at lower HAc

concentration (< 50 ppm), the corrosion rate increased from 0.1 to 1 mm/y in the

range of rotation speed from 0 to 6000 rpm. This is in agreement with other

researchers data that there is a minimum of HAc concentration to increase corrosion

rate.

83

4

3

2

1

HAc( ppm)

Rot

atio

n sp

eed

(rpm

)

300250200150100500

6000

5000

4000

3000

2000

1000

0 23

Temp (deg. C) 22Hold Values

> – – – – < 0

0 11 22 33 4

4

(mm/y)Cr

HAc( ppm) = 265.332rot (rpm) = 3779.08Cr (mm/y ) = 4.05036

Figure 4.14 Response surface contours of corrosion rate as a function of HAc

concentration and rotation rate at 22oC at pH 4.

4.4.4 Maximum corrosion rate

As described previously, the response observation is useful to determine location of

maximum corrosion rate which indicates scaling temperature. The use of RSM has

been successful in visualizing the maximum corrosion rate along the range of

variables setting. The contour plot in Figure 4.15 show that the maximum corrosion

rate is dependent on the operating conditions.

Corr. rate (mm/y)

84

9

8

7

6

5

4

Temperature (deg. C)

Rot

atio

n sp

eed

(rpm

)

807060504030

6000

5000

4000

3000

2000

1000

0

HAc (ppm) 170Hold Values

> – – – – – – < 3

3 44 55 66 77 88 9

9

(mm/y)rateCorr.

our Plot of Corr. rate (mm/y vs Rotation speed (, Temperatur

Temperature (deg. C) = 74.8455Rotation speed (rpm) = 4102.49Corr. rate (mm/y) = 9.59862

Figure 4.15 Response surface contours of corrosion rate as a function of temperature

and rotation speed at 170 ppm HAc concentration at pH 4.

The response surfaces calculated by second order model can also be used to

indicate the maximum point on the range of independent variable analytically.

Calculations of the maximum point using the first derivative of the mathematical

function gave the maximum corrosion rate. The maximum points are located in

condition where the first derivative of the response surface equals to zero. Calculating

first derivative of equation 4.1 to each independent variable (T, HAc, N) results:

TY / 68.126 + 0.039(HAc) + 0.00017 (N) –(T) = 0 (4.2)

HAcY / 231.58 + 1.89(T) - 0.002(N) – (HAc) = 0 (4.3)

NY / 4417.33 - 1.84(HAc) - 7.45(T) – (N) = 0 (4.4)

Thus, to calculate the coordinate of the critical point, it is necessary to solve those

three equations and to find the T, HAc and N values. By solving the equations, the

maximum corrosion rate of the model was found to occur at HAc 380 ppm, rotation

speed 3000 rpm, and temperature 80oC. The corrosion rate at this condition is 11.0

mm/y.

Corr. rate (mm/y)

85

4.5 Design of Experiment for Analyzing Corrosion Rate Model at pH 5.5

The design of experiment selected for this experiment was CCD. This design

methodology has been found as the best methodology as discussed previously for

experiments at pH 4. The CCD used in this experiment is presented in Table 4.4. A

total of eighteen observations were involved in this design. The independent variables

used in these experiments are temperature, rotation speed and HAc concentration to

predict corrosion rate model at pH 5.5.

Table 4.4 CCD experimental design for CO2 corrosion at pH 5.5.

Variable code Experimental variables No

of run HAc

T

N

HAc

(ppm)

T

(oC)

N

(rpm)

Exp. results

(Yi)

1 1 1 1 270 70 4000 7

2 -1 1 1 70 70 4000 5.2

3 1 -1 1 270 35 4000 4.2

4 -1 -1 1 70 35 4000 3.2

5 1 1 -1 270 70 1000 5.2

6 -1 1 -1 70 70 1000 4

7 1 -1 -1 270 35 1000 3.1

8 -1 -1 -1 70 35 1000 2.4

9 3 0 0 340 50 2000 5.9

10 -3 0 0 0 50 2000 2

11 0 3 0 170 80 2000 5.3

12 0 -3 0 170 22 2000 2.4

13 0 0 3 170 50 6000 5.9

14 0 0 -3 170 50 0 2.3

15 0 0 0 170 50 2000 4.5

16 0 0 0 170 50 2000 4.6

17 0 0 0 170 50 2000 4.7

18 0 0 0 170 50 2000 4.7

86

4.5.1 Generalization of corrosion prediction model at pH 5.5

The corrosion prediction model at pH 5.5 was fitted using second-order polynomial

equation (Equation 2.68). The model proposed as calculated by Equation 2.71 and

2.72 for the response is given below.

Y = -2.3890 + 0.0090(HAc) + 0.1064(T) + 0.0006(N) - 0.0007(T)2 +

0.0001(HAc)(T) (4.5)

Where;

Y = corrosion rate (mm/y)

HAc = concentration of HAc (ppm)

T = temperature (oC)

N = rotation speed (rpm)

4.5.2 Prediction of CO2 corrosion model at pH 5.5

The average corrosion rate obtained from the experiments (Yi) is compared to data

from corrosion predictions (ŷ) as presented in Table 4.5. From the difference, it can

be seen that there is a reasonable predictions between corrosion data experiments and

predictions.

87

Table 4.5 Comparison between corrosion data experiments and corrosion data

predictions for CO2 corrosion at pH 5.5.

Variable code Experimental

variables

No

of

run HAc

(ppm)

T

(oC)

N

(rpm)

HAc

(ppm)

T

(oC)

N

(rpm)

Exp.

results

(Yi)

Predct.

(ŷ)

Error

(Yi-ŷ)

1 1 1 1 270 70 4000 7 7.2 -0.2

2 -1 1 1 70 70 4000 5.2 5.2 -0.0

3 1 -1 1 270 35 4000 4.2 4.7 -0.5

4 -1 -1 1 70 35 4000 3.2 3.2 -0.0

5 1 1 -1 270 70 1000 5.2 5.2 -0.0

6 -1 1 -1 70 70 1000 4 3.4 0.6

7 1 -1 -1 270 35 1000 3.1 3.3 -0.2

8 -1 -1 -1 70 35 1000 2.4 1.9 0.5

9 3 0 0 340 50 2000 5.9 5.3 0.6

10 -3 0 0 0 50 2000 2 2.6 -0.6

11 0 3 0 170 80 2000 5.3 5.5 -0.2

12 0 -3 0 170 22 2000 2.4 2.2 0.2

13 0 0 3 170 50 6000 5.9 5.6 0.3

14 0 0 -3 170 50 0 2.3 2.9 -0.6

15 0 0 0 170 50 2000 4.5 4.4 0.1

16 0 0 0 170 50 2000 4.6 4.4 0.2

17 0 0 0 170 50 2000 4.7 4.4 0.3

18 0 0 0 170 50 2000 4.6 4.4 0.2

88

4.5.3 Analysis variance

Table 4.6 shows the analysis of variance for corrosion in saturated CO2 solution using

CCD methodology for corrosion rate at pH 5.5 as calculated from Reference [84].

Table 4.6 Analysis of variance for CCD model regression for the fitted models.

Source DF Seq

SS

Adj

SS

Adj

MS F P

Regression 9 32.3158 32.3158 3.59064 10.13 0.005

Linear 3 31.4462 26.5343 8.84476 24.95 0.001

Square 3 0.5830 0.5711 0.19035 0.54 0.674

Interaction 3 0.2866 0.2866 0.09552 0.27 0.845

Residual Error 6 2.1266 2.1266 0.35443

Lack-of-Fit 5 2.1216 2.1216 0.42431 84.86 0.082

Pure Error 1 0.0050 0.0050 0.00500

Total 15 34.4423

R-Sq = 97.29%

4.6 Evaluation of Model Adequacy

As shown in Figure 4.16 to Figure 4.18, it can be seen that the normal plotting of the

residual meets the model’s assumptions for normal probability (Figure 4.16),

independency (Figure 4.17) and uncorrelated variance (Figure 4.18). Figure 4.19

shows the correlation between observed experimental data and predicted values with

an acceptable level of 94%. These results imply a satisfactory mathematical

description of the corrosion rate data.

89

1.00.50.0-0.5-1.0

99

95

90

80

7060504030

20

10

5

1

Residual

Perc

ent

Figure 4.16 Normal plot of residuals.

16151413121110987654321

0.75

0.50

0.25

0.00

-0.25

-0.50

Observation Order

Res

idua

l

Figure 4.17 Residuals versus order of data.

765432

0.75

0.50

0.25

0.00

-0.25

-0.50

Fitted Value

Res

idua

l

90

Figure 4.18 Residuals versus fitted values.

R2 = 0.94

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

Predicted values (mm/y)

Obs

erve

d va

lues

(mm

/y)

Figure 4.19 The relationship between observed and predicted values

of the corrosion rate model at pH 5.5.

4.7 Verification with Experimental Data and Corrosion Prediction Software

Experimental data of Ismail [61] is used for the range of HAc concentration from 0 –

300 ppm. The comparison between the RSM model and the experiment data is shown

in Figure 4.20 and Figure 4.21. A good fit was observed of the effects of HAc

concentration and temperature.

The effect of temperature on corrosion rate for the case of HAc concentration 20

ppm was also verified using ECE [75] software (Figure 4.22). The predicted corrosion

rate calculated by ECE software has R2 of 95%, correlation of 97% and standard error

of 0.2 (± 0.15 mm/y). A HAc comparison between the RSM model and those

calculated by Freecorp software [88] is presented in Figure 4.23. It shows a coefficient

determination of 99%, correlation of 99%, and standard error estimation of 0.05 (±

0.03 mm/y). The summaries of statistical performances of the models are presented in

Appendix 2.

91

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300

HAc (ppm)

Cor

rosi

on ra

te (m

m/y

)

Exp model

Figure 4.20 Corrosion rate at varying concentrations of HAc; a comparison between

RSM model and Ismail’s experimental data in 1 bar CO2, 22°C, pH 5.5, and 1000

rpm.

0

0.5

1

1.5

2

2.5

22 32 42 52 62

Temperature (oC)

Cor

rosi

on ra

te (m

m/y

)

Exp. Model

Figure 4.21 Corrosion rate at varying temperature; a comparison between RSM

model and Ismail’s experimental data in 1 bar CO2, blank solution, pH 5.5, and

stagnant condition.

92

0

0.5

1

1.5

2

2.5

3

22 32 42 52 62 72

Temperature (oC)

Cor

rosi

on ra

te (m

m/y

)

ECE Model

Figure 4.22 Corrosion rate at varying temperature; a comparison between RSM model

and ECE in 1 bar CO2, 20 ppm HAc, pH 5.5, and stagnant condition.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

25 75 125 175 225 275

HAc (ppm)

Cor

rosi

on ra

te (m

m/y

)

Free corp. Model

Figure 4.23 Corrosion rate at varying concentrations of HAc, a comparison between

Model and Freecorp in 1 bar CO2, 35°C, pH 5.5, and 1000 rpm rotation speed.

93

4.8 Analysis and Interpretation of Response Surface of CO2 Corrosion at pH 5.5

Response of corrosion rate at pH 5.5 can be seen in the form of surface contour to

show the simultaneous effects of variables tested as presented in Figures 4.24 - 4.26.

RSM model equations are also used to calculate maximum corrosion rate caused by

scaling temperature and limiting current density indicated by critical values of the

model.

4.8.1 Effects of temperature and HAc concentration

The interaction between HAc concentration and temperature was studied using

contour plot as presented in Figure 4.24. From Figure 4.24, it can be observed that

there is an increase in corrosion rate due to increase in temperature and HAc

concentration and temperature. At the higher temperature (80oC), an increase in HAc

concentration causes a significant increase in the corrosion rate.

4

3

2

1

0

HAc( ppm)

Tem

pera

ture

(de

g. C

)

300250200150100500

80

70

60

50

40

30

Rot. speed (rpm) 0Hold Values

> – – – – < 0

0 11 22 33 4

4

mm/y)CR(

HAc( ppm) = 332.898Temp (C ) = 78.4307CR( mm/y) = 4.86533

Figure 4.24 Response surface contours of corrosion rate as a function of temperature

and HAc concentration at pH 5.5 and stagnant condition.

Corr. rate (mm/y)

94

4.8.2 Effects of temperature and rotation speed

Figure 4.25 shows the effects of temperature and rotation speed on corrosion rate. As

can be seen in Figure 4.25, corrosion rate increases with increasing temperature and

rotation speed. The corrosion rate increases sharply at high temperature (80oC). At

30oC, increasing the rotation speed from 1000 to 6000 rpm caused the corrosion rate

to increase from 1 to 2 mm/y. However at 80oC, there is an increase of corrosion rate

by 2 mm/y. These observations indicate that there was a synergism effect between

temperature and rotation speed.

4

3

2

1

Temperaure (deg. C)

Rot

atio

n sp

eed

(rpm

)

807060504030

6000

5000

4000

3000

2000

1000

0

HAc( ppm) 0Hold Values

> – – – – – < 0

0 11 22 33 44 5

5

mm/yCR(

Temp (C) = 79.3488rot (rpm) = 5882.65CR( mm/y) = 4.97140

Figure 4.25 Response surface contours of corrosion rate as a function of temperature

and rotation speed at pH 5.5 without HAc.

4.8.3 Effects of HAc concentration and rotation speed

The relationship between HAc concentration and rotation speed presented in contour

graph is as shown in Figure 4.26. At the specified test conditions, corrosion rate

shows an increase with increasing HAc concentration and rotation speed. Similarly,

an increase in temperature and rotation speed (Figure 4.25) also causes corrosion rate

to increase. From the contour graph in Figure 4.26, it can be concluded that the effect

of HAc concentration and rotation speed on corrosion rate is to cause corrosion rate to

Corr. rate (mm/y)

95

reach a stationary (maximum values) which shows the effect of limiting current

density and film formation.

3

2

1

0

HAc( ppm)

Rot

atio

n sp

eed

(rpm

)

300250200150100500

6000

5000

4000

3000

2000

1000

0

Temp. (deg. C) 22Hold Values

> – – – < 0

0 11 22 3

3

mm/y)CR(

HAc( ppm) = 336.822rot (rpm) = 5972.64CR( mm/y) = 3.59540

Figure 4.26 Response surface contours of corrosion rate as a function of temperature

and rotation speed at temperature 22oC and pH 5.5.

4.8.4 Maximum corrosion rate

The response surfaces calculated by second order model as explained previously

(corrosion at pH 4) is applied to predict the maximum corrosion rate at pH 5.5. The

first derivate of the mathematical function of corrosion model at pH 5.5 gives the

following results:

TY / 0)()(004.0)(051.001.75 TNHAc (4.6)

NY / 0)()(107.34)(37.122.4134 NTHAc (4.7)

HAcY / 0)()(007.0)(434.249.304 HAcNT (4.8)

By solving the equations, the maximum corrosion rate obtained from the model is

10 mm/y. These results have shown that the response surface has a maximum point

Corr. rate (mm/y)

96

outside the experimental range of the independent variables. The maximum

coordinates for three independent variables can be found beyond these experimental

variables.

4.9 Design of Experiment to Predict Corrosion Rate at varying pH

The RSM regression model was used to study simultaneous effects of variables tested

(HAc, T, N, pH). The model used FFD to find empirical relationship among variables.

The first step was conducted by identifying historical data variables to find the

trending of the CO2 corrosion model. In order to evaluate the model performance, the

model was verified with published experimental data and corrosion software

calculation.

4.9.1 Identification corrosion trend

The relationship between corrosion rate and H+ ions concentration from 0.1 to 0.001

mol/m3 based on mechanistic theory is shown in Figure 4.27. This concentration of H+

ions corresponds to conditions at pH 4 to pH 6. It is shown that corrosion rate will

increase exponentially when H+ concentration increases. At the low concentration of

H+ ions, the corrosion rate increases significantly; while at the higher concentration of

H+ ions, the corrosion rate increases slowly.

97

Figure 4.27 Simulated corrosion rate for a range of ions H+ concentration from 0.1

mol/m 3 to 0,001 mol/m3 (corresponds to pH 4 to pH 6) at 1 bar and static.

A design experiment involving four independent variables where full factorial design

methodology was applied to predict the effect of pH on corrosion rate. The factors

that were analyzed were: pH, temperature, HAc concentration and rotation speed.

Table 4.7 shows the matrix arrangement used to study the effects of those four

independent variables on corrosion rate using 3 % NaCl saturated CO2 solution. The

selected design experiment model was based on the most adequate model fitting. It

was found that second order model had the best fitting of the corrosion rate data.

4.10 Design of Experiment to Study Effect of pH on Corrosion Rate

Table 4.7 shows the corrosion rate as effects of different concentration of HAc, T

and N at various pH 4. The test was conducted for 1.5 hours and recorded the reading

every 15 minutes. The corrosion rate measurements are calculated based on the

average corrosion rate during 1.5 hours measurements.

Cor

rosi

on ra

te (m

m/y

)

H+ concentration

98

Table 4.7 Experimental design to calculate model regression constant.

Coded variables Natural variables

No

of

run pH Temp HAc Rot

pH

Temp

(oC)

Hac

(ppm)

N

(rpm)

Exp.

results

(mm/y)

1 -1 -1 -1 -1 4 22 0 1000 1.3

2 1 -1 -1 -1 5.5 22 0 1000 1.2

3 -1 1 -1 -1 4 60 0 1000 5.2

4 1 1 -1 -1 5.5 60 0 1000 2.9

5 -1 -1 1 -1 4 22 60 1000 2.6

6 1 -1 1 -1 5.5 22 60 1000 1.8

7 -1 1 1 -1 4 60 60 1000 6.9

8 1 1 1 -1 5.5 60 60 1000 3.8

9 -1 -1 -1 1 4 22 0 6000 2.8

10 1 -1 -1 1 5.5 22 0 6000 2.3

11 -1 1 -1 1 4 60 0 6000 5.1

12 1 1 -1 1 5.5 60 0 6000 4.9

13 -1 -1 1 1 4 22 60 6000 3.1

14 1 -1 1 1 5.5 22 60 6000 2.9

15 -1 1 1 1 4 60 60 6000 6.8

16 1 1 1 1 5.5 60 60 6000 5.8

17 -1 0 0 0 4 35 40 3000 5.0

18 1 0 0 0 5.5 35 40 3000 3.7

19 0 -1 0 0 5 22 40 3000 2.8

20 0 1 0 0 5 60 40 3000 5.4

21 0 0 -1 0 5 35 0 3000 4.0

22 0 0 1 0 5 35 60 3000 4.3

23 0 0 0 -1 5 35 40 1000 3.0

24 0 0 0 1 5 35 40 6000 4.9

99

4.10.1 Generalization of model

The application of RSM to study effects of pH on CO2 corrosion using 24 factorial

design taken from Table 4.7 yields the following regression equation. This equation is

an empirical relationship between independent variables as given in the following

equation:

Y = -9.5966 + 1.5759(pH) + 0.4585(T) + 0.0361(HAc) + 0.0001(N) -

0.1720(pH)2 - 0.0032(T)2 - 0.0230(pH)(T) - 0.0067(pH)(HAc) + 0.0002(pH)(N)

+ 0.0001(T)(HAc) (4.9)

Where;

Y = corrosion rate (mm/y)

pH = pH

HAc = concentration of HAc (ppm)

T = temperature (oC)

N = rotation speed (rpm)

4.10.2 Prediction of CO2 corrosion model at various pH

The corrosion rate measured from the experiments (Yi) is compared with data from

corrosion predictions (ŷ) is presented in Table 4.8. From the difference, it can be seen

that there is a reasonable agreement between the experimental corrosion data and

predicted values.

100

Table 4.8 Comparison between corrosion data experiments and corrosion data

predictions

Experimental variables No

of

run

pH

Temp(oC) HAc

(ppm)

N

(rpm)

Exp.

results

(Yi)

Predct.

(ŷ)

Error

(Yi-ŷ)

1 4 22 0 1000 1.3 1 0.3

2 5.5 22 0 1000 1.2 0.4 0.8

3 4 60 0 1000 5.2 5 0.2

4 5.5 60 0 1000 2.9 3.1 -0.1

5 4 22 60 1000 2.6 2 0.6

6 5.5 22 60 1000 1.8 0.8 1

7 4 60 60 1000 6.9 6.6 0.3

8 5.5 60 60 1000 3.8 4 -0.2

9 4 22 0 6000 2.8 1.7 1.1

10 5.5 22 0 6000 2.3 2.3 0

11 4 60 0 6000 5.1 5.4 -0.3

12 5.5 60 0 6000 4.9 4.7 0.2

13 4 22 60 6000 3.1 2.5 0.6

14 5.5 22 60 6000 2.9 2.4 0.5

15 4 60 60 6000 6.8 6.9 -0.1

16 5.5 60 60 6000 5.8 5.5 0.3

17 4 35 40 3000 5.0 4.8 0.2

18 5.5 35 40 3000 3.7 3.8 -0.1

19 5 22 40 3000 2.8 2.1 0.7

20 5 60 40 3000 5.4 5.5 -0.1

21 5 35 0 3000 4.1 3.8 0.3

22 5 35 60 3000 4.3 4.5 -0.2

23 5 35 40 1000 3 3.3 -0.3

24 5 35 40 6000 4.9 4.6 0.3

101

4.10.3 Analysis variance

Table 4.9 shows the analysis of variance for corrosion in saturated CO2 solution using

two level of full factorial designs (FFD) methodology for studying corrosion rate. The

analyses of variance (ANOVA) described the confidence level of predicted

parameters involved in the regression model. According to the ANOVA, the effect of

linear and square in model regression has a significant value (for significance of

95%). But, the effect of interaction is significant at 93% significance level. Overall,

the RSM model represents 97 % of experimental data.

Table 4.9 Analysis of variance for FFD model regression for the fitted models.

Source DF Seq

SS

Adj

SS

Adj

MS F P

Regression 14 0.940032 0.940032 0.067145 23.06 0.000

Linear 4 0.740227 0.831772 0.207943 71.43 0.000

Square 4 0.148696 0.148747 0.037187 12.77 0.001

Interaction 6 0.051109 0.051109 0.008518 2.93 0.072

Residual Error 9 0.026202 0.026202 0.002911

Total 23 0.966234

R-Sq = 97.29%

4.11 Prediction and Verification of Corrosion Rate at pH 5

The effects of rotation speed on corrosion rate of carbon steel in solutions containing

3% sodium chloride, pH 5, temperature 60oC at different HAc concentration from

both experimentation and calculation are shown in Figure 4.28 to Figure 4.30. The

results show that the corrosion rate for both experimental and predictions increase

with increasing rotation speed and HAc concentration. All figures show good

agreement with each other. The results also reveal that at higher rotation speed,

corrosion rate reaches a plateau that may be associated to limiting current density.

102

This shows that electrochemical reactions and diffusion reaction may govern the

corrosion rate.

0

1

2

3

4

5

6

7

0 1000 2000 3000 4000 5000 6000

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Exp.

Figure 4.28 Effect of rotation speed on corrosion rate; a comparison between RSM

model and Martin’s experiments in 1 bar CO2, 60oC, 20 ppm HAc, and pH 5.

0

1

2

3

4

5

6

7

0 1000 2000 3000 4000 5000 6000Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Exp.

Figure 4.29 Effect of rotation speed on corrosion rate; a comparison between RSM

model and Martin’s experiments in 1 bar CO2, 60oC, 40 ppm and HAc, pH 5.

103

0

1

2

3

4

5

6

7

0 1000 2000 3000 4000 5000 6000Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Exp.

Figure 4.30 Effect of rotation speed on corrosion rate; a comparison between RSM

model and Martin’s experiments in 1 bar CO2, 60oC, 60 ppm HAc, and pH 5.

4.12 Prediction and Verification of Corrosion Rate at pH 6.

The effects of rotation speed on corrosion rate of carbon steel in 3% sodium chloride

solutions at pH 6 and temperature 60°C, at varying HAc concentration from both

experimentation and calculation are shown in Figure 4.31 to Figure 4.33. The

corrosion rate is observed to increase with the increase in rotation speed and HAc

concentration. Both, data predicted by the RSM model and experimental data show a

steady corrosion increase at higher rotation speed. This trend is similar to the

corrosion rate at pH 5. This shows that corrosion rate is not only controlled by charge

transfer, but also by mass transfer.

104

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1000 2000 3000 4000 5000 6000

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Exp.

Figure 4.31 Effect of rotation speed on corrosion rate; a comparison between RSM

model and Martin’s experiments in 1 bar CO2, 60oC, 20 ppm HAc, and pH 6.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1000 2000 3000 4000 5000 6000

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Exp.

Figure 4.32 Effect of rotation speed on corrosion rate; a comparison between RSM

model and Martin’s experiments in 1 bar CO2, 60oC, 40 ppm HAc, and pH 6.

105

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1000 2000 3000 4000 5000 6000

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Exp.

Figure 4.33 Effect of rotation speed on corrosion rate; a comparison between RSM

model and Martin’s experiments in 1 bar CO2, 60oC, 60 ppm HAc, pH 6.

4.13 Prediction of the Effect of pH on Corrosion rate

The effect of pH on corrosion rate was studied in solutions saturated with CO2 with

the addition of HAc in the pH range from 4 to 5.5 using RSM. The results are shown

in Figure 4.34 to Figure 4.37. The RSM model is compared to Nesic’s experimental

data, which had shown a good fit. As the pH was increased from 4 to 6, the corrosion

rate decreased from 0.8 mm/y to 0.5 mm/y.

106

00.10.20.30.40.50.60.70.80.9

4 4.5 5 5.5 6pH

Cor

rosi

on ra

te (m

m/y

)

Exp Model

Figure 4.34 Corrosion rate at varying pH; a comparison RSM model

with Nesic’s experimental data in1 bar, 20oC, and stagnant condition.

4.13.1 Effect of pH and temperature on CO2 corrosion

Figure 4.35 shows the result of corrosion prediction by RSM at various pH and

temperature. These calculations were performed at temperatures from 25 to 60oC at

varying pH in the range of 4 to 5.5. From the figure, it is observed that corrosion rate

increases rapidly at the temperature of around 50oC. While at lower temperatures

(25oC), the corrosion rate increases slowly (from 3 to 3.5 mm/y). Corrosion rate

seems to be affected more by temperature rather than pH.

107

6.0

5.5

5.04.5

4.0 3.5

3.0

pH

Tem

pera

ture

(de

g. C

)

5.45.25.04.84.64.44.24.0

60

55

50

45

40

35

30

25

HAc (ppm) 30Rot. speed (rpm) 3500

Hold Values

> – – – – – – < 3.0

3.0 3.53.5 4.04.0 4.54.5 5.05.0 5.55.5 6.0

6.0

(mm/y)Cor. rate

pH = 4.33153Temperature (deg. C) = 56.9805Cor. rate (mm/y) = 6.20338

Figure 4.35 Response surface contours for corrosion rate as a function of temperature

and pH at HAc at 30 ppm and rotation speed at 3500 rpm.

4.13.2 Effect of pH and HAc on CO2 corrosion

2.502.25

2.00

1.75

1.50

1.25

pH

HA

c (p

pm)

5.45.25.04.84.64.44.24.0

60

50

40

30

20

10

0

Temp. (deg. C) 25Rot. speed (rpm) 1000

Hold Values

> – – – – – – < 1.00

1.00 1.251.25 1.501.50 1.751.75 2.002.00 2.252.25 2.50

2.50

(mm/y)Cor. rate

pH = 4.06642HAc (ppm) = 57.6266Cor. rate (mm/y) = 2.63063

Figure 4.36 Response surface contours for corrosion rate as a function of HAc and

pH at 25oC and rotation speed at 1000 rpm.

Corr. rate (mm/y)

Corr. rate (mm/y)

108

Figure 4.36 presents the corrosion rate obtained using RSM model for varying HAc

concentration and pH in the range 4 to 5.5. In general, the corrosion rate increases

with increasing HAc concentration in the specified range of pH. The graph shows that

corrosion rate decreases with increasing pH. In this prediction, the maximum

corrosion rate is at pH 4 and 60 ppm HAc.

4.13.3 Effect of pH and rotation speed on CO2 corrosion

Figure 4.37 shows a correlation between pH, rotation speed and corrosion rate. In

Figure 4.37, it can be seen that corrosion rate increases with increasing rotation speed.

The corrosion rate increases faster at pH 4 compared to pH 5. It is also observed that

at higher rotation speed (4000 – 6000 rpm), the corrosion rate is almost constant even

though pH increases. This indicates the flow independent limiting current region

caused by rotation speed.

2.5

2.5

2.0 1.5

pH

Rot

atio

n sp

eed

(rpm

)

5.45.25.04.84.64.44.24.0

6000

5000

4000

3000

2000

1000

Temp. (deg. C) 25HAc (ppm) 0

Hold Values

> – – – < 1.0

1.0 1.51.5 2.02.0 2.5

2.5

(mm/y)Cor. rate

pH = 5.45938Rotation speed (rpm) = 5874.09Cor. rate (mm/y) = 2.81274

Figure 4.37 Response surface contours for corrosion rate as a function of rotation

speed and pH at 25oC and blank solution.

Corr. rate (mm/y)

109

4.14 Discussions: CO2/HAc Corrosion

The results of the various concentrations of HAc with different variables tested such

as T and N in CO2 saturated solution are discussed in these sections below.

4.14.1 Effects of temperature and HAc concentration on corrosion rate

The effects of temperature and HAc concentration on carbon steel in CO2

environments, as modeled by RSM, are presented in Figure 4.12 and Figure 4.24. The

figures show that an increase in temperature and HAc concentration leads to an

increase in corrosion rate. The increase in corrosion rate is related to the role of HAc

as a source of additional species providing protons and a new cathodic reaction via the

direct reduction of undissociated HAc [62]. The mechanism of the dissolved HAc in

CO2 corrosion can also be correlated to the concentration of undissociated HAc

present in the solution as described by Nafday [17]. The effects of HAc in low

concentration (6-60 ppm) had been proposed by Crolet et al. [64] to inhibit the anodic

(iron dissolution). They argued that the increase in the rate of corrosion was due to an

inversion in the bicarbonate/acetate ratio. At this inversion point, HAc is the

predominant acid compared to carbonic acid, and becomes the main source of acidity.

Several researchers who have conducted experiments involving HAc confirmed that

the presence of HAc in the range of 10 – 340 ppm causes higher corrosion rate

compared to without HAc [61]. The increased corrosion as an effect of temperature

and HAc concentration was also observed by Ismail [61], James [5] and Nesic et al.

[6].

The electrochemical behavior of carbon steel with the presence of HAc resulted:

decreasing pH, increasing cathodic limiting current, and decreasing Ecorr. Further,

Nesic et al. [6] argued that the cathodic reaction will become the rate determining step

and the limitation was due to diffusion of proton to the steel surface rather than

electron transfer. There is a proof that HAc can increase the cathodic reaction rate by

hydrogen evolution reaction process if the concentration is significant.

As shown by the RSM model, the corrosion rate at pH 4 is higher than at pH 5.5.

The effect is proportional to the amount of HAc presented. At pH 5.5, the corrosion

rate also increases when HAc concentration is increased. However, the average

110

corrosion rate at pH 5.5 is lower than the average corrosion rate at pH 4. These

observations suggest that H+ ions are the predominant factor that contributes to

corrosion rate.

4.14.2 Effects of temperature and rotation speed.

As observed in the Figure 4.13, corrosion rate increases with increasing temperature

and rotation speed. It can be seen that at 80oC, increasing the rotation speed did not

produce significant effect on corrosion rate. These observations indicate that

increasing temperature will eliminate the effect of rotation speed on corrosion rate.

This is due to the formation of limiting current density as the effect of interaction with

temperature.

It has been recognized that temperature strongly influences corrosion rate. It can

increase or decrease corrosion rate depending on films properties produced during

corrosion reactions. As can be seen from Figure 4.13, the corrosion rate is higher at

lower temperatures (< 60 °C) compared to the higher temperatures. An increase of the

corrosion rate can be related to the degree of solubility of the species in solution since

higher solubility of FeCO3 slows down the formation of the protective film. Song [90]

stated that, at temperatures below 60oC, hydrogen evolution took part as a rate

determining step and carbonate scale did not form well. The film was detached and

porous, which gave little protection and cannot be detected. In this condition, the

kinetics of film formation was faster and corrosion rate was under charge-transfer

control. Above 60°C, the protectiveness of the iron carbonate layer increases with

temperature as the solubility of iron carbonate decreases. Thus, the corrosion rate is

reduced. However, at higher temperatures, there is a direct reaction between steel and

water to produce dense and protective films [91]. Therefore, in this condition

corrosion rate may be governed by film formation.

111

4.14.3 Scaling temperature

Based on the literature reviews [61, 91], temperature is known to increase corrosion

rate until the temperature reaches a maximum value called scaling temperature.

Beyond this temperature, the corrosion rate will decrease or becomes constant.

Factors affecting the scaling temperature are pH, HAc concentration and rotation

speed. The scaling temperature as an effect of pH predicted by the RSM model is

presented in Figure 4.38 and 4.39 below.

20

30

40

50

60

70

80

3.8 4.3 4.8 5.3 5.8

pH

Tem

pera

ture

(o C)

Model Exp.

Figure 4.38 Effects of pH on scaling temperature as calculated by RSM in 1 bar and

stagnant (Experimental data were taken from reference [61]).

From Figure 4.38 and Figure 4.39, it can be seen that higher pH tend to decrease

scaling temperature. This observation is supported by several researchers [6, 17], who

related this phenomena to film formation where higher pH tend to favor film

precipitation.

112

20

30

40

50

60

70

80

3.8 4.3 4.8 5.3 5.8

pH

Tem

pera

ture

(o C

)

Model Exp.

Figure 4.39 Effects of pH on scaling temperature as calculated by RSM in 1 bar CO2,

360 ppm HAc, and stagnant (Experimental data were taken from reference [61]).

0

20

40

60

80

100

120

140

0 20 40 60 80 100

HAc (ppm)

Tem

pera

ture

(o C)

pH 4 pH 5.5

Figure 4.40 Effects of HAc on scaling temperature as calculated by RSM

in 1 bar CO2, and stagnant.

Scaling temperature is also influenced by HAc concentration. As shown in Figure

4.40 and Figure 4.41, higher HAc concentration will increase scaling temperature.

Figure 4.40 shows that the influence of pH on scaling temperature, where lower pH

causes the scaling temperature to increase. The finding are also supported by M.C.

Ismail [61]. A comparison between calculations from RSM and Ismail’s experimental

data is presented in Figure 4.41. George [62] explained that the presence of HAc can

113

interrupt the film formation and increase scaling temperature. Surface analyses

investigation indicated that HAc concentration has decreased the thickness of the film.

Vennesa et al. [66] observed that HAc can retard the time to reach scaling

temperature. She related this effect to an increase in the area of corrosion. She argued

that the prime factor which influences film formation is the degree of solubility.

However, since the solubility of iron acetate is much higher than iron carbonate’s,

therefore, the protective film formation by iron acetate cannot readily occur. Without

the formation of a stable protective film, the corrosion rate of steel in CO2

environment can remain high [14].

40

45

50

55

60

65

70

0 20 60 360HAc (ppm)

Scal

ing

tem

pera

ture

(o C)

Exp. Model

Figure 4.41 Effects of HAc on scaling temperature as calculated by RSM in 1 bar

CO2, stagnant, and pH 6 (Experimental data were taken from reference [61]).

4.14.4 Effects of rotation speed on corrosion rate

Figure 4.14 (pH 4) and Figure 4.26 (pH 5.5) present a second order model of response

surface relating the effect of rotation speed and HAc concentration on corrosion rate.

Different corrosion rate are observed at different HAc concentration and rotation

speed, for both pH conditions.

The effect of flow on corrosion rate has been studied by Silverman et al.[33-35].

They explained that flow increases corrosion due to a combination of mechanical

114

effects due to water motion, and electrochemical effects of corrosion. Higher velocity

is directly associated with higher turbulence that promotes mixing in the solution.

This affects both the corrosion rate of the bare steel surface and the precipitation rate

of iron carbonate. Prior to any film formation, high velocity will lead to increased

corrosion rate. The transport of cathodic species toward the steel surface is enhanced

by turbulent transport. At the same time the transport of Fe2+ ions away from the steel

surface also increases, leading to a lower concentration of Fe2+ ions at the steel

surface. This results in higher surface supersaturation and thus precipitation rate

becomes lower [34].

Further, Singer [51] explained that flow-induced corrosion is a type of corrosion

that is caused by a combination between mechanical and electrochemical effects.

Mechanical effect due to water motion causes impingement that leads to metal

removal and material abrasion, and increases wall shear stress as shown in Figure

4.42. Water that flows to the surface can also wear the corrosion product film or

create shear stress to the surface. In conclusion, the researchers [33, 34, 51] found that

parameters influenced flow induced corrosion are hydrodynamic boundary layer and

rate of momentum transfer which affects on mass transfer of reactants.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200Rotation speed (rpm)

Wal

l she

ar s

tress

(g c

m–1

s–2

)

Figure 4.42 Effect of rotation speed on wall shear stress [74].

115

4.14.5 Flow independent limiting current

There is also threshold value of rotation speed. These phenomena can be studied by

using cathodic scan polarization. Through cathodic polarization, Martin [60] observed

that at specific rotation value the cathodic current behavior will show diffusion

behavior termed as limiting current density. In this case, Rothman and Mendoza as

cited by Ismail [61] classified the effect of flow in two regions; flow dependent

limiting current and flow independent limiting current. Flow dependent limiting

current is correlated with diffusion of main electrochemical species of H+, H2CO3, and

HAc; while flow independent limiting current is related to chemical reaction product

as an effect of corrosion process. The effect of temperature and HAc concentration on

rotation speed threshold is presented in Figure 4.43. This graph was obtained by

solving RSM equations 4.2 to 4.4.

1000

2000

3000

4000

5000

6000

7000

0 50 100 150 200 250 300 350

HAc (ppm)

Thre

shol

d ro

tatio

n sp

eed

(rpm

)

22C 50oC

Figure 4.43 Effects of HAc on threshold rotation speed as calculated by RSM in 1 bar

CO2, pH 4 and stagnant.

116

4.14.6 Effects of pH

The effects of pH on corrosion rate as calculated by RSM can be seen in Figure 4.36

and Figure 4.37. At low pH, corrosion rate increases sharply. According to Garsany et

al. [65], in relating to HAc, the increase of corrosion rate will increase proportionally

to the concentration of undissociated HAc in the brine solution. Joosten et al. [2], also

examined the effect of pH on corrosion rate in synthetic seawater solution with HAc.

They found a localized corrosion when 600 ppm HAc was added.

In CO2 environments, pH is influenced by changing the H+ ions concentration,

temperature, pressure, and ionic strength [17]. pH is affected by dissolved iron

bicarbonate; pH will increase when there is an increase of ion bicarbonate, The

reduction in corrosion rate pH increases can be explained by the properties of the

protective film. At higher pH, the carbonate film becomes thicker, more dense and

protective. Thus, the passivity of carbon steel lies within the pH range of the

carbonate/bicarbonate formation [92]. Observations as described by Figure 4.37 show

that as pH increases from 4 to 5, the anodic reaction rate also increases; this

observation is consistent with Bockris’s iron dissolution mechanism [12]. However a

further increase of pH from 5 to 6, did not increase either the anodic reaction rate or

corrosion rate. At higher pH, the cathodic reaction and the limiting current was

retarded by the increasing pH. Hoffmeister [29] recorded that at pH 5.8 the corrosion

rate did not reduce significantly, which reflected a relatively porous, detached and un-

protective carbonate film. These properties may be related to fast formation of the

film. Thus, the effect of concentration of dissolved iron bicarbonate, as an initial

corrosion product is important to predict corrosion rate at certain pH value [50].

4.15 Comparison between Experimental Corrosion Rates and Commercial

Predictive Models

The results from the experiments are compared to Freecorp [88], which is a

commercial prediction software. The Freecorp combines electrochemical theories

which consist of partial cathodic and anodic processes on the metal surface. This

model provides the most realistic conditions of aqueous CO2 system. The total

corrosion rate is calculated based on the mixed-potential theory under activation or

117

mass control by taking account the oxidation of iron and reduction of hydrogen ions,

water reductions, carbonic acid and acetate ions reductions. The comparisons are

shown in Table 4.10 (pH 4) and Table 4.11 (pH 5.5). Based on the comparison results

on Table 4.10 at conditions: 20 ppm HAc concentration, temperature 60 – 70oC and

low rotation speed, it shows that the corrosion rate calculated by the RSM model is

less precise compared to blank solution, middle temperature and high rotation speed

conditions. At the middle temperature, high rotation speed conditions, the Freecorp

and RSM model shows precise values (st. error 0.1). Table 4.11, conditions at pH 5.5,

shows that Freecorp does not show a good standard error of corrosion rate at low

temperature and high rotation speed condition. While good agreements of standard

error occurred in middle and high temperature as well as 20 ppm HAc concentration

conditions.

Table 4.10 Summary of the performance of predictive model pH 4

RSM models Predictions vs Freecorp Test Conditions Level

R2 Correlation Standard error

High 0.80 0.88 0.4

Medium 0.83 0.90 0.18

Temperature

(oC)

Low 0.87 0.94 0.27

High 0.90 0.97 0.30

Medium 0.90 0.97 0.30

Rotation speed

(rpm)

Low 0.90 0.97 0.18

High 0.85 0.8 0.10

Medium 0.82 0.94 0.20

HAc

(ppm)

Low 0.89 0.98 0.37

118

Table 4.11 Summary of the performance of predictive model at pH 5.5

RSM models Predictions vs Freecorp Test Conditions Level

R2 Correlation Standard error

High 0.81 0.89 0.30

Medium 0.90 0.95 0.18

Temperature

(oC)

Low 0.80 0.88 0.18

High 0.95 0.94 0.22

Medium 0.96 0.93 0.28

Rotation speed

(rpm)

Low 0.96 0.93 0.44

High 0.85 0.80 0.20

Medium 0.82 0.94 0.20

HAc

(ppm)

Low 0.89 0.98 0.15

In general, the RSM models consider a feasible comparable with the Freecorp

model calculation as described by statistics performance attached in Appendix 2. It

can be summarized that the models, in average, have coefficient determination of 87

% that shows 87 % of the software prediction can be explained by the RSM model.

The trend similarity indicated by correlation provides a value of 92%. However, the

scatter observed between RSM model and predictive model contribute to predictive

error of 24%. Comparing RSM model with experimental data from reference [61]

(Appendix 2c – 2d), the results does not show a significant different to the

comparison with Freecorp. It has coefficient determination 88 %, correlation 94% and

standard error 0.26.

From the statistical data explained above it can be seen that it is found uncertainties

indicated by standard error between RSM and Freecorp or experimental data. Those

errors come from the following:

Freecorp calculates corrosion rate under activation control of cathodic

reactions. It will show a higher results when corrosion is controlled by film

formation.

119

The total rate of corrosion involving several species is equal to the sum of the

corrosion caused by those individual species. This will cause the higher value

corrosion rate due to interactions between the species that change the

electrochemical behavior.

Freecorp model does not consider carbon content of specimen, scan rate

polarization, surface roughness of specimen, and Tafel slope. Although those

parameters are often neglected, those parameters, in fact, have effects in

corrosion rate.

Limitations of the LPR test methodology, test parameters setting and

experimental set up. The uncertainties of corrosion measurements based on

this electrochemical method have been recorded to significant value (27 %)

[17].

Fe2+ concentration, Cl- ions concentrations, and actual water chemistry are not

known in detail. The effect of Fe2+ concentration and water chemistry

properties influence iron carbonate precipitation which can affect corrosion

rate.

Those factors that affect the error have been recorded to contribute absolute

experimental error of 34% as calculated by O. A. Nafday [17].

4.16 Conclusion

Based on the experimental predictions using response surface methodology, the

following conclusion can be made:

4.16.1 Experimental design

Second order polynomial regression model is adequate to represent the data

for all responses obtained. The RSM corrosion model, which includes the

effects of temperature, HAc and rotation speed has a quadratic function and

can be fitted well with the literatures and corrosion program software.

The mathematical models obtained by RSM can be used to calculate stationary

value analytically. The stationary values are useful to determine mechanistic

120

corrosion process such as scaling temperature, flow independent limiting

current and flow dependent limiting current.

The RSM is capable in predicting corrosion rate by using limited numbers of

experiments.

4.16.2 Regression model relationship

A second order relationship has been found between HAc concentration, rotation

speed and temperature on corrosion rate; while an exponential relationship is found

between pH, HAc concentration, rotation speed and temperature on corrosion rate. As

expected, all dependent variables have a high positive correlation with corrosion rate.

While pH, and interaction between pH and HAc concentration show a negative

correlation. The curve describes that a high HAc concentration and temperature will

increase corrosion rate.

4.16.3 Effects of HAc, temperature and rotation speed based on RSM model

Increasing HAc concentration causes increased corrosion rate for a given

temperature and rotation speed at both pH 4 and pH 5.5.

Increasing temperature causes increased corrosion rate for a given HAc

concentration and rotation speed at both pH 4 and pH 5.5.

Increasing rotation speed causes increased corrosion rate for a given

temperature and HAc concentration at both pH 4 and pH 5.5.

Highest corrosion rate occurred at the middle of temperature, HAc

concentration and rotation speed at pH 4. While at pH 5.5, the maximum

corrosion rate located on the high temperature, high rotation speed and high

HAc concentration.

At low rotation speed, the effect of temperature is more dominant as compared

to the effects of HAc concentration at pH 4. The dominant effect of

temperature compared to rotation speed was also observed at low HAc

concentration at pH 5.5. These trends did not find in pH 5.5 where both

121

temperature and HAc concentration have the same role in contributing

corrosion rate.

Corrosion product formation is an important parameter in defining corrosion

model regression that can be used to determine initial identification for

corrosion predictions.

Based on RSM data and supported by the works of previous researches,

rotation speed has little effect on the corrosion rate of carbon steel in CO2

environment (at pH 4 and pH 5.5).

Corrosion rate has a weak dependence on combination rotation speed with

HAc concentration and temperature at both pH 4 and pH 5.5.

Interaction simultaneously between HAc concentration, temperature and

rotation did not have a significant value in contributing corrosion rate.

122

CHAPTER 5

EFFECTS OF HAc AND H2S IN CO2 ENVIRONMENT

The results and discussions of the effect of H2S and HAc are presented in the

following sections. The experimental studies carried out in this work include: identify

initial of H2S corrosion model, conduct experimental works based on design of

experiment, generate experimental data to find empirical constant parameters used in

the RSM model equation and evaluate the empirical RSM model prediction. In order

to find a trending of experimental data, it was used H2S corrosion mechanistic theory

developed by Nesic et al. [62] and Song et al. [90]. Then, the data trend is used to fit

the experimental data to obtain parametric relationships for the empirical model.

5.1 Initial Identification of Corrosion Rate Model

Figure 5.1 presents the simulated corrosion rate of carbon steel due to the presence of

H2S in CO2 environment, calculated based on Equation 3.9. The individual effects of

H2S on corrosion rate under two different conditions were simulated i.e. free of film

formation and with film formation. In film free formation (dot line), the corrosion is

found to be controlled by activation process. On the other hand, when film formation

exists, corrosion is controlled by diffusion limiting current. As can be seen in the

graph, in film free condition (straight line) the corrosion rate will increase if H2S

concentration increases. In contrast to film formation condition, an increase in H2S

concentration will reduce the corrosion rate. These results are in agreement with

Gaute et al. [93] who predicted in parabolic model represent carbon steel metal loss in

the CO2/H2S environments. Heusler [94] also proposed a parabolic model to predict a

model for the relationship metal loss with exposure time in aqueous H2S conditions.

123

Figure 5.1 Simulated corrosion rate as a function of H2S concentration in conditions

where film dominated reaction or activation dominated reaction.

5.2 Design of experiment for Analyzing CO2/H2S/HAc Corrosion Model

This study proposes the use of RSM to construct a CO2/H2S/HAc corrosion model. A

CCD with RSM has been applied to study the effects of H2S and HAc in CO2

corrosion. An experimental design matrix as presented in Table 5.1 was used to study

the effects of independent variables such as, HAc, rotation speed, and temperature to

predict the corrosion rate of carbon steel in CO2/H2S environments.

H2S (mol/m3)

Cor

rosi

on ra

te (m

m/y

)

Activation control

Film formation control

124

Table 5.1 Experimental design matrix of independent variables to study corrosion rate

in CO2/H2S/HAc environment (at 300 ppm H2S).

Coded variables Natural variables Corrosion

rate

(mm/y)

HAc

T

N

HAc

(ppm)

T

(oC)

N

(rpm)

Exp.

results

(Yi)

1 1 1 108 70 4000 3.9

-1 1 1 28 70 4000 3.0

1 -1 1 108 35 4000 3.2

-1 -1 1 28 35 4000 2.2

1 1 -1 108 70 1000 3.7

-1 1 -1 28 70 1000 2.9

1 -1 -1 108 35 1000 3.0

-1 -1 -1 28 35 1000 2.0

1.7 0 0 136 50 2000 4.0

-1.7 0 0 0 50 2000 2.0

0 1.7 0 68 80 2000 3.4

0 -1.7 0 68 22 2000 2.4

0 0 1.7 68 50 6000 2.8

0 0 -1.7 68 50 500 2.4

0 0 0 68 50 2000 2.8

0 0 0 68 50 2000 2.5

0 0 0 68 50 2000 2.6

0 0 0 68 50 2000 2.7

5.3 Parameter EstimationBased on mechanistic identification, the corrosion rate in

CO2/H2S/HAc model was assumed to be a second-order polynomial as the best

fitting. Thus, by fitting this curve to the experimental data, a regression model of

the following equation was obtained:

125

Y = 1.6612 + 0.0046(HAc) - 0.0103(T) + 0.0001(N) + 0.0001(HAc)2 +

0.0001(T)2 (5.1)

Where;

Y = Corrosion rate (mm/y)

T = temperature (oC)

HAc = concentration of HAc (ppm)

N = rotation speed (rpm)

Table 5.2 presents variant analysis of the second order model regression model

used to fit corrosion behavior calculated RSM theory. From the Table5.2, it can be

seen that overall the regression models have significant values of 97%. The

regression effects of temperature, HAc, and rotation speed show a significant level of

F-test (p-value <0.05). There are also significant effects of square RSM model (92%)

while interaction model is less significant in modeling this regression. Therefore it

can be concluded that in general, there is a significant correlation between the RSM

model and experimental result.

Table 5.2 Analysis of variance for CCD RSM model regression.

Source DF Seq

SS

Adj

SS

Adj

MS F P

Regression 9 5.864 5.862 0.651 28.94 0.00

Linear 3 5.600 0.044 0.0146 0.65 0.61

Square 3 0.248 0.247 0.082 3.65 0.08

Interaction 3 0.016 0.016 0.005 0.24 0.86

Residual Error 6 0.136 0.135 0.022

Lack-of-Fit 5 0.091 0.090 0.018 0.40 0.8

Pure Error 1 0.045 0.045 0.045

Total 15 6

R-Sq = 97.7%

126

5.4 Prediction of CO2 corrosion model at pH 4

The average corrosion rate of carbon steel observed from the experiments (Yi) is

compared with data from corrosion predictions (ŷ) as presented in Table 5.3. From

the difference, it can be seen that there is a reasonable predictions between corrosion

data experiments and predictions.

Table 5.3 Comparison between corrosion data from experiments and predicted

corrosion data

Coded variables Natural variables Corrosion rate (mm/y)

HAc

T

N

HAc

(ppm)

T

(oC)

N

(rpm)

Exp.

results

(Yi)

Predicted

(ŷ)

Error

Yi – ŷ

1 1 1 108 70 4000 3.9 4.0 -0.1

-1 1 1 28 70 4000 3 3.0 0

1 -1 1 108 35 4000 3.2 3.3 -0.1

-1 -1 1 28 35 4000 2.2 2.1 0.1

1 1 -1 108 70 1000 3.7 3.7 0

-1 1 -1 28 70 1000 2.9 2.7 0.2

1 -1 -1 108 35 1000 3 3.1 -0.1

-1 -1 -1 28 35 1000 2 1.9 0.1

1.7 0 0 136 50 2000 4 4.0 0

-1.7 0 0 0 50 2000 2 2.1 -0.1

0 1.7 0 68 80 2000 3.4 3.5 -0.1

0 -1.7 0 68 22 2000 2.4 2.3 0.1

0 0 1.7 68 50 6000 2.8 2.9 -0.1

0 0 -1.7 68 50 500 2.4 2.5 -0.1

0 0 0 68 50 2000 2.8 2.6 0.2

0 0 0 68 50 2000 2.5 2.6 -0.1

0 0 0 68 50 2000 2.6 2.6 0

0 0 0 68 50 2000 2.7 2.6 0.1

127

Relationship between observed experimental data and predicted values is shown

in Figure 5.2 that shows a correlation with an acceptable level of 98%. These results

imply a satisfactory mathematical description of the corrosion rate data.

R2 = 0.980.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0.1 0.15 0.2 0.25 0.3

Predicted values (mm/y)

Obs

erve

d va

lues

(mm

/y)

Figure 5.2 A relationship between observed and predicted values of the RSM

corrosion rate model.

5.5 Verification of the RSM Model with Experimental Data and Corrosion

Prediction Software

5.5.1 Effect of HAc concentration on corrosion rate in CO2/H2S/HAc

environments

The corrosion rate of various concentrations of HAc obtained from RSM model is

presented in Figure 5.3. A comparison of the corrosion rate calculated by the RSM

model to the predicted corrosion rate by Freecorp software [88] at 35oC, 300 ppm

H2S/CO2 saturated solution and 10 rpm rotation speed shows a good relationship in

the range 40 to 160 ppm of HAc . The results show a standard error of 0.23 (0.18

mm/y). The correlation is 0.98 and the R2 is 0.97.

128

11.5

2

2.5

3

3.5

4

4.5

5

40 60 80 100 120 140 160HAc (ppm)

Cor

rosi

on ra

te (m

m/y

)

ModelFree corp.

Figure 5.3 Corrosion rate at varying concentrations of HAc. A comparison between

RSM model and Freecorp. corrosion software in 1 bar, 300 ppm H2S, 35oC,

and 10 rpm.

5.5.2 Effect of temperature on corrosion rate in CO2/H2S/HAc environments

Effect of temperature on corrosion rate in CO2/H2S/HAc environments is presented in

Figure 5.4. The effect of temperature on linear polarization sweep was studied using

3% NaCl solutions saturated with 300 ppm H2S/CO2, pH 4, 1000 rpm and of the

temperature was varied from 30oC to 80oC. The results calculated by RSM model and

those predicted by ECE [75] are shown in Figure 5.4. The comparison between the

RSM model and ECE shows R2 of 97, correlation of 98 and standard error estimation

of 0.1 (0.08 mm/y).

129

0

0.5

1

1.5

2

2.5

3

3.5

30 40 50 60 70 80

Temperature (oC)

Cor

rosi

on ra

te (m

m/y

)

Model ECE

Figure 5.4 Corrosion rate at various temperature. A comparison between RSM model

and ECE in 1 bar, 300 ppm H2S, 10 ppm HAc, and 1000 rpm.

5.5.3 Effect of rotation speed on corrosion rate in CO2/H2S/HAc environments

Corrosion rates of carbon steel at various rotation speed for exposures up to 1 hour is

also shown in Figure 5.5. Looking at corrosion values predicted by the software, it

can be observed that an increase in the rotation speed from 200 to 4000 rpm has

increased the corrosion rate from 1.9 to 2.4 mm/y. The graph also shows that the

values calculated by the RSM model are lower than the values predicted by Freecorp

[88], however, the values are still reasonable. A comparison between the predicted

and calculated values shows an R2 of 0.80, standard error estimation of 0.07 and

correlation of 0.90. This indicates that the RSM model’s prediction is less accurate.

130

1.51.61.71.81.9

22.12.22.32.42.5

200 700 1200 1700 2200 2700 3200 3700

Rotation speed (rpm)

Cor

rosi

on ra

te (m

m/y

)

Model Free corp.

Figure 5.5 Corrosion rate at various rotation speed. A comparison between RSM and

Freecorp in 1 bar, 300 ppm H2S, 50oC, and 5 ppm HAc.

5.6 Analysis and Interpretation of Response Surface of CO2/H2S/HAc Corrosion

The following results present the contour surface that shows effects of combinations

variables tested on CO2/H2S/HAc corrosion model.

5.6.1 Combined effects of rotation speed and HAc on corrosion rate

The simultaneous combined effect of rotation speed and HAc on corrosion rate is

presented in Figure 5.6. As illustrated in the figure, the corrosion rate increased

slowly in the presence of low concentration of HAc (0 – 60 ppm). In the presence of

10 ppm of HAc, rotation speed does not seem to have a very strong influence on

corrosion rate. The corrosion rate increased to 2.5 mm/y in the range of HAc

concentration from 0 to 60 ppm. While the corrosion rate increased to 4 mm/y in the

presence of 120 ppm of HAc. These observations are in good agreement with

previous study [60, 61, 63] where the increase of corrosion rate were related with

extra cathodic reaction and direct reduction of HAc.

131

4.0

3.5

3.0

2.5

HAc (ppm)

Rot

atio

n sp

eed

(rpm

)

120100806040200

6000

5000

4000

3000

2000

1000

0

Temp (deg. C) 51Hold Values

> – – – < 2.5

2.5 3.03.0 3.53.5 4.0

4.0

(mm/y)Corr. rate

Contour Plot of Corr. rate (mm/y) vs C3, C1

Figure 5.6 Response surface contours for corrosion rate as a function of HAc and

rotation speed at 51oC and 300 ppm H2S.

5.6.2 Combined effects of rotation speed and temperature on corrosion rate

The effect of rotation speed and temperature is presented in Figure 5.7 as calculated

by RSM. The combined effect of rotation speed and temperature has increased the

corrosion rate to 3.6 mm/y. The combined effects of rotation speed and temperature

on corrosion rate indicates a logarithmic model. At lower temperature (25oC), the

effect of rotation speed shows an increase in the corrosion rate up to 2.7 mm/y. The

same trends are observed at all of the temperature conditions.

132

3.6

3.3

3.0

2.7

2.4

Temperature (deg. C)

Rot

atio

n sp

eed

(rpm

)

807060504030

6000

5000

4000

3000

2000

1000

0

HAc (ppm) 68Hold Values

> – – – – < 2.4

2.4 2.72.7 3.03.0 3.33.3 3.6

3.6

(mm/y)Corr. rate

Figure 5.7 Response surface contours of corrosion rate as a function of rotation speed

and temperature at 68 ppm HAc concentration and 300 ppm H2S.

5.6.3 Combined effects of HAc and temperature on corrosion rate

The combined effect of temperature and HAc on corrosion rate in 300 ppm H2S/CO2

environment is presented in Figure 5.8. The figure shows that effects of HAc

concentration on corrosion rate follow the same trend as the effects of temperature.

Both temperature and HAc concentration increase corrosion rate according to a

polynomial pattern.

133

4.0

3.5

3.0

2.5

2.0

HAc (ppm)

Tem

pera

ture

(de

g. C

)

120100806040200

80

70

60

50

40

30

Rot. speed (rpm) 3000Hold Values

> – – – – – < 2.0

2.0 2.52.5 3.03.0 3.53.5 4.04.0 4.5

4.5

(mm/y)Corr. rate

Figure 5.8 Response surface contours for corrosion rate as a function of HAc and

temperature at 3000 rpm rotation speed.

5.7 Mechanistic Study of CO2/H2S/HAc Corrosion

The corrosion rate of carbon steel at various HAc concentration in the CO2/H2S

system was also studied by LPR and EIS technique and the results are presented in

Figure 5.9. As observed in the graph, the corrosion rate increases consistently at the

experimental conditions of HAc concentration ranging from 0 – 180 ppm. In other

words, HAc controls the corrosion rate. At 180 ppm of HAc, the corrosion rate

increases by 0.5 times.

The study of surface characteristics of H2S/CO2/HAc corrosion was carried out

using EIS technique and the results are presented in Figure 5.10. Figure 5.10

illustrates characteristics of the Nyquist plot at 80 ppm and 130 ppm of HAc in a 3%

NaCl solution with 300 ppm H2S and saturated CO2. As seen in the graph, there is a

depressed semi-circle at high frequencies, which indicates a double layer capacitance.

134

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

0 20 50 80 130 180

HAc (ppm)

Cor

rosi

on ra

te (m

m/y

)LPREIS

Figure 5.9 Corrosion rate at various HAc concentration in 1 bar, 300 ppm H2S, and

22oC. (A comparison between LPR and EIS results).

Figure 5.10 Nyquist plot to calculate corrosion rate as a function of HAc

concentration in 1 bar, 300 ppm H2S, and 22oC.

The Nyquist plot shows a decreasing charge transfer resistance with increasing of

HAc concentration. This means that corrosion rate increases as the concentration of

0

5

10

15

20

25

30

35

40

10 30 50 70 90 110 130

Z' (ohm.cm2)

Z" (o

hm.c

m2 )

Blank 80 ppm HAc 130 ppm HAc

Rp

135

HAc is increased (Figure 5.10) and the effect is proportional to the amount of HAc

added. As shown in Figure 5.10, the charge transfer resistance decreases from 129 to

99 when 130 ppm of HAc is introduced into solution.

From the EIS data, several values of solution resistance, charge transfer resistance,

capacitance film formed and corrosion rate can be described in the form of equivalent

circuit parameters as presented in Figure 5.11. Table 4.55 shows the parameters

values of solution resistance, charge transfer resistance, capacitance film formed and

corrosion rate obtained from the experiments using EIS technique.

Figure 5.11 Typical equivalent circuit for a mixed diffusion and charge transfer

control used to represent the experimental conditions.

Table 5.4 Circuit parameters result for CO2/H2S/HAc corrosion at various HAc

concentration.

Electrical circuit Blank 80 (ppm) 130 (ppm)

Rp (ohms.cm²) 104 88 74

Capacitance (F) 3.32x10-3 6.18x10-3 6.92x10-3

Depression angle 30.56 38.23 35.23

Corr. rate (mm/y) 1.3 1.5 1.6

5.8 Potentiodynamic Polarization Test

The polarization sweeps were conducted to study the effect of H2S on CO2 corrosion.

The result is presented in Figure 5.12. The figure shows that there are some

differences between the polarization graphs of carbon steel corrosion in CO2 and in

136

300 ppm H2S/CO2 system. H2S gas increases CO2 corrosion rate and also increases

cathodic Tafel slope. This finding was also observed by Zang et al. [95] when they

conducted experiments in conditions with a constant H2S/CO2 partial pressure ratio of

1.7.

-900

-850

-800

-750

-700

-650

-600

0.001 0.01 0.1 1 10Current density (mA/cm2)

Pot

entia

l (m

V)

CO2300 ppm CO2/H2S

Figure 5.12 Potentiodynamic sweeps in CO2 solution with/without H2S in 1 bar, 22oC,

300 ppm H2S, pH 4, and stagnant.

Effects of HAc addition on Tafel slope can be seen in Figure 5.13. Observations

from Figure 5.13 indicates that there is no significant effect of HAc addition on

anodic Tafel slopes in 300 ppm H2S/CO2 system. However, the cathodic slope shows

an increase of reaction process in the presence of HAc.

137

Figure 5.13 Potentiodynamic sweeps in 300 ppm H2S/CO2 saturated solution at

various HAc concentrations in 1 bar, 22oC, 300 ppm H2S, pH 4, and stagnant.

5.9 CO2/H2S/HAc Corrosion Discussions

Based on data calculations using RSM model, the following sections are discussed

effects of the variables tested on corrosion in H2S/CO2 environment.

5.9.1 Model evaluation

In these experiments, the results show that second-order polynomial model is the most

appropriate model to predict CO2/H2S/HAc corrosion pattern. Using the polynomial

model, the curve pattern such as linear or exponential pattern can be obtained. Figure

5.3 shows a linear pattern at low HAc concentration, while a polynomial model is

shown at higher concentrations of HAc. Flow rate influences corrosion rate in a linear

pattern in the range of rotation speed tested from 0 to 6000 rpm. The effect of

temperature shows a similar trend as the effects of HAc on corrosion rate.

Temperature shows a linear pattern at lower temperature range and a polynomial

pattern at higher temperature range (Figure 5.4).

Residual analysis method was applied to validate all proposed RSM models. It

was simplified by analyzing the p-value of each RSM model as presented in the

ANOVA (Table 5.2). The p-value for the 2nd polynomial model is 0.08. The

-830

-810

-790

-770

-750

-730

-710

-690

-670

-650

-630

0.0001 0.001 0.01 0.1 1 10

Current (mA/cm2)

Pot

entia

l (m

V)

Blank 80 ppm HAc180 ppm HAc

Icorr

Anodic

reaction

Cathodic

reaction

138

confidence level of all RSM models is within 97 %, which indicates that the RSM

models represent 97% of the experimental data.

5.9.2 Combined effect of rotation speed and HAc

The corrosion rate as a function of different rotation speed and HAc is shown in

Figure 5.6. As observed in the graph, corrosion rate increases significantly with

increasing speed and the effect is more dominant at higher HAc concentration. At

lower HAc concentration, the corrosion rate increases slowly.

At higher rotation speed and higher HAc concentration, the effect of rotation

speed is to cause the corrosion rate to increase significantly. The higher corrosion rate

may be related to electrochemical and hydrodynamic effects of the solution.

Increasing the HAc concentration and rotation speed accelerate the electrochemical

reaction transfer in agreement with George [86]. A faster rotation speed can also

reduce thickness of the boundary layer of water next to a metal surface. This thinner

boundary layer allows the dissolved species to corrode the metal surface more quickly

in agreement with Gaute [93].

5.9.3 Combined effect of temperature and rotation speed

From Figure 5.7, it has shown that the maximum corrosion rate of carbon steel

increases by 50% with increasing temperature from 20 to 80°C. However, the

corrosion rate starts to reach a plateau as temperature increases, especially in the

temperature range more than 70oC. This observation may be related to the formation

of FeS and FeCO3 film. The corrosion rate, which is charge-transfer controlled at

room temperature (22°C) becomes mass-transfer limiting current controlled at higher

temperatures.

The combined effect of rotation speed and temperature on both the corrosion rate and

the scaling temperature can be visually illustrated by RSM model. As can be observed in

Figure 5.7, at 300 ppm of H2S gas concentration, the corrosion rate varies with rotation

speed. As predicted by RSM, at the lower rotation speed, there is minimum effect of

139

temperature on corrosion rate. When the rotation speed is higher, the corrosion rate

increases significantly with increasing temperature. This finding is in agreement with the

findings by Fragiera et al. [96], who also found that at higher temperature, localized

corrosion tend to occur.

5.9.4 The combined effect of HAc and Temperature

The potentiodynamic experimental results for different HAc concentrations in and

temperature in CO2/H2S/HAc mixed corrosion environments are given in Figure 5.8.

The experimental results show that as HAc concentration increases, the corrosion rate

also increases. The HAc acts as a provider of protons and at the same time adds a new

cathodic reaction via direct reduction of undissociated HAc [86]. The effect is

proportional to the amount of HAc added. Thus, it can be concluded that HAc

concentration is a dominant factor in determining corrosion behavior. In addition, the

increase of cathodic reaction caused by HAc concentration do not change cathodic

Tafel slope.

5.9.5 Flow independent and flow dependent limiting current

It has been commonly accepted that the increase in corrosion rate due to an increase

in rotation speed will become stagnant at a certain rotation speed called flow

independent limiting current. But, at this condition, there is no significant effect of

rotation speed on limiting current density. A mathematical relationship of

temperature, HAc concentration and rotation speed was obtained using RSM model.

Equation 5.1, which was obtained by fitting the experimental matrices in Table 5.1

shows that a curved slope pattern that corresponds to flow independent limiting

current cannot be obtained. The equation shows a constant relationship between

rotation speed and curved slope.

140

5.9.6 Scaling temperature and chemical reaction limiting current in

H2S/CO2/HAc corrosion

The response surfaces calculated by quadratic models can also be used to indicate the

maximum point on the range of independent variable analytically. The determination

of scaling temperature can be performed by calculated using first derivate of the

mathematical function of Equation 5.1. The maximum points are located at conditions

where the first derivative of the response surface equals to zero as presented in

Equation 5.2 and Equation 5.3. Figure 5.14 below shows the dependency of scaling

temperature on HAc concentration. Based on the RSM model in Figure 5.14, the

scaling temperature did not form. The corrosion rate continues to increase as

temperature increases. It can be concluded that within 1 hours of exposure time, there

was no film formation. The corrosion process was under activation control.

(T 1.661+0.0046(HAc) - 0.0103(T)+ 0.0001(N) + 0.0001(HAc)2 + 0.0001(T)2) = 0

(5.2)

T = -14.7143 - 0.11471(HAc) = 0 (5.3)

Figure 5.14 Corrosion rate gradient of RSM model at varying temperature and

without HAc.

Temperature (oC)

Cor

rosi

on ra

te g

radi

ent

141

Chemical reaction limiting current can be obtained using RSM model, by

calculating first derivative of the mathematical function of the RSM model (Equation

5.1 ).

(HAc 1.661+0.0046(HAc)- 0.0103(T) + 0.0001(N) + 0.0001(HAc)2 +

0.0001(T)2)= 0 (5.4)

HAc = 0.0023) - 0.00005(T) (5.5)

Analytical observation from Equations 5.4 and 5.5 indicates that chemical reaction

limiting current did not happen in this range of experiments. The slope of the

mathematical function shows a tendency to increase with increasing HAc

concentration. This means that the corrosion rate will increase continuously within the

tested variables (Figure 5.15)

Figure 5.15 Corrosion rate gradient of the RSM model at varying HAc concentration

and 22oC.

5.9.7 Effects of H2S on CO2 corrosion mechanism

Effects of H2S on CO2 corrosion are presented in Figure 5.12. It is observed that

corrosion rate increases in the presence of H2S gas. In pure CO2 solution, corrosion

rate is controlled by charge transfer reaction. The addition of 300 ppm of H2S caused

HAc (ppm)

Cor

rosi

on ra

te g

radi

ent

142

the corrosion rate to increase. H2S can accelerate corrosion rate by increasing cathodic

reaction rate. Kvarekval [50] explained that the increased corrosion rate is caused by

sulfide ions or by H2S acting as a catalyst for hydrogen evolution and governs

diffusion of proton donors. Further, he reported that H2S can also increase hydrogen

evolution rate without taking part in the net reaction. The H+ ions from H2S molecule

can penetrate steel surface to create a pitting corrosion which can increase corrosion

rate [95]. Figure 5.13 also reveals that anodic polarization behavior does not change

significantly with the addition of hydrogen sulfide. Anodic Tafel slope is consistent

with iron dissolution in CO2 solution. However, cathodic Tafel slope has increased

significantly.

The addition of H2S also gives impact to diffusion limiting current density of CO2

corrosion. From the experiments using EIS technique (Figure 5.10), the presence of

tail in the Nyquist plot has been detected, which indicates mass transfer effect in the

process. However, the scan polarization analyses show activation control reaction.

Thus, the behavior of cathodic limiting current density consists of chemical reaction

and diffusion process.

5.9.8 Effects of HAc on CO2/H2S corrosion mechanisms

EIS corrosion measurement technique was used to study the effects of HAc

concentration on CO2/H2S corrosion. Figure 5.10 demonstrates the effects of adding

80 ppm and 180 ppm of HAc into a 300 ppm H2S/CO2 saturated solution at pH4. As

can be seen from the figure, the impedance diagram shows a depressed semi-circle at

high frequencies, which indicates a double layer capacitance. This condition, as

quoted by Bai [97], suggests that there are heterogeneous surface and non-uniform

distribution of current density.

At 80 ppm and 180 ppm HAc, the steady state impedance diagram demonstrates a

smaller depressed semi-circle with similar characteristics. The decrease in

polarization resistance Rp from EIS measurements indicates an increase in corrosion

rate with increasing HAc concentration. Moreover, there was a tail observed in the

experiments (Figure 5.10). These results suggest that the corrosion mechanism is a

diffusion process control in the presence of HAc. The same characteristic is found in

143

the experiments without HAc. From the description in Figure 5.10, it can be

concluded that the corrosion reaction of H2S/CO2 system is dominated by HAc

reactions.

The effects of adding HAc was also studied using potentiodynamic test. From the

test, it has been shown that additional HAc concentration do not have significant

effect on anodic Tafel slope (Figure 5.13). Figure 5.13 indicates that cathodic slope

increases the reaction process with increasing HAc concentration, but do not change

cathodic Tafel slope. This means that HAc is the dominant factor that governs the

reaction process.

5.10 Conclusion

5.10.1 Mechanism corrosion rate in CO2/H2S/HAc system

The presence of 0.3 mbars of H2S in 0.7 bars of CO2 causes an average of

approximately 10% increase in the corrosion rate compared to H2S free.

H2S accelerates corrosion rate by increasing the cathodic Tafel slope.

The introduction of 180 ppm of HAc to the H2S/CO2 gaseous mixture causes

the corrosion rate to increase sharply in the temperature range 40–80°C.

The anodic polarization behavior did not change significantly with the

addition of hydrogen sulfide.

HAc is the dominant factor that governs the reaction process in CO2/H2S

system. The behavior of cathodic reaction consists of chemical reaction and

diffusion process.

Based on RSM model, the scaling temperature, limiting current density and

limiting chemical reaction did not form in the range of experiments.

HAc has the most dominant effect on corrosion process followed by

temperature and rotation speed.

144

5.10.2 Model regressions

The results have shown that second-order polynomial model can be used to predict

CO2/H2S/HAc corrosion pattern adequately. This study has proven that CCD can be

applied to predict CO2 corrosion process with reasonable planning and execution.

Thus, the statistical analysis and evaluations of data could be proved analytically. The

results from the experiments are compared to Freecorp [88] as provided in the

appendix 2.e. It can be summarized that the models, in average, have coefficient

determination 70 % correlation 82% and predictive error 18 % relative to the Freecorp

model.

145

CHAPTER 6

CONCLUSION AND RECOMMENDATION

6.1 Conclusion

The RSM regression models for the carbon steel corrosion in CO2 environments

involving HAc, temperature and rotation speed as parameters have been successful

developed and validated with experimental data and commercial predictive models.

The RSM is efficient in determining empirical relationship of the variables tested

simultaneously. In the form of mathematical equations, the effects of independent

variables will be easily identified and developed. Furthermore, using mathematical

operations, certain conditions such as stationary conditions can be calculated

analytically to identify scaling temperature, limiting current density and independent

flow conditions.

The results have shown that second-order polynomial model can be used to

predict CO2/H2S/HAc corrosion pattern adequately. CCD is appropriate to design

experiments in CO2/H2S environments. The comparison results show that all of the

RSM models are acceptable statistically with average R2 of 93%, average standard

error 0.2 and average correlation of 95%.

In general, effects of individual variables can be concluded as follows:

Increasing HAc concentration causes increased corrosion rate for a given

temperature and rotation speed at both pH 4 and pH 5.5.

Increasing temperature causes increased corrosion rate for a given HAc

concentration and rotation speed at both pH 4 and pH 5.5.

Increasing rotation speed causes increased corrosion rate for a given

temperature and HAc concentration at both pH 4 and pH 5.5.

146

6.2 Scope of Model

Since the model is developed based on experimental data only, there are several

limitations of the RSM that makes it suitable only for parameters used in the

experiments conditions. The presented RSM model is for uniform corrosion in

experimental test conditions; therefore it does not predict localized corrosion in other

environments. The RSM model does not account for higher partial pressure of CO2,

film formations, the effect of high chloride concentrations, oxygen, elemental sulfur

or any other conditions that may contribute to corrosion rate. Therefore, it is

recommended to use this RSM model under corrosion prediction at testing conditions.

6.3 Future Research

The RSM model considers pH, temperature and rotation speed in combination with

HAc concentration to predict corrosion at atmospheric parameters. However, in field

conditions, there are other operating variable at higher pressure such as oxygen,

sodium chloride and other species that affect corrosion. Therefore it is recommended

that further study to be conducted by using the same technique but including other

variables such as O2, inhibitor, NaCl, and any other species that promote corrosion at

higher CO2 pressure.

Future work on optimization should be started with complex variables. The

complex variables can be selected using design experiments to determine the

important variables that can be developed further

Different design experiments can be selected for the same case to determine the

performance of the experimental design, to investigate the effect of the experimental

design to the developed RSM model.

In order to optimize experimental research, it is necessary to choose appropriate

experimental design to find an adequate mathematical function. Thus, preliminary

study should be conducted in relation to obtaining a predicted model. Preliminary

studies can be started by initial identification, examination of collected experimental

data and studying history of the data to construct mathematical models.

147

As an alternative to experimental model, RSM can be combined with the

application of neural network. Also, RSM can be applied with mechanistic theory to

simplify calculations and to select the most dominant variables involved in corrosion,

for screening the appropriate model.

148

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APPENDIX 1

1.a Corrosion rate at pH 4

0

1

2

3

4

5

6

7

8

0 20 40 60 80Time (minutes)

Cor

rosi

on ra

te (m

m/y

)

270 ppm, 4000 rpm270 ppm, 1000 rpm70 ppm, 1000 rpm70 ppm, 4000 rpm

Figure A.1 Average corrosion rate of carbon steel in CO2 saturated NaCl solution: pH

4, 35oC, different HAc concentration and rotation speed.

0

2

4

6

8

10

12

0 20 40 60 80Time (minutes)

Cor

rosi

on ra

te (m

m/y

)

270 ppm, 4000 rpm270 ppm, 1000 rpm70 ppm, 4000 rpm70 ppm, 1000 rpm

158

Figure A.2 Average corrosion rate of carbon steel in CO2 saturated NaCl solution: pH

4, 70oC, different HAc concentration and rotation speed.

0

2

4

6

8

10

12

0 20 40 60 80Time (minutes)

Cor

rosi

on ra

te (m

m/y

)

340 ppm, 2000 rpm170 ppm, 6000 rpm170 ppm, 2000 rpm170 ppm, 500 rpm blank, 2000 rpm

Figure A.3 Average corrosion rate of carbon steel in CO2 saturated NaCl solution: pH

4, 50oC, different HAc concentration and rotation speed.

1.b Corrosion rate at pH 5.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 20 40 60 80Time (minutes)

Cor

rosi

on ra

te (m

m/y

)

270 ppm, 4000 rpm270 ppm, 1000 rpm70 ppm, 4000 rpm70 ppm, 1000 rpm

159

Figure A.4 Average corrosion rate of carbon steel in CO2 saturated NaCl solution: pH

5.5, 35oC, different HAc concentration and rotation speed.

0

1

2

3

4

5

6

7

8

0 20 40 60 80Time (minutes)

Cor

rosi

on ra

te (m

m/y

)

270 ppm, 4000 rpm270 ppm, 1000 rpm70 ppm, 4000 rpm70 ppm, 1000 rpm

Figure A.5 Average corrosion rate of carbon steel in CO2 saturated NaCl solution: pH

5.5, 70oC, different HAc concentration and rotation speed.

0

1

2

3

4

5

6

7

0 20 40 60 80Time (minutes)

Cor

rosi

on ra

te (m

m/y

)

340 ppm, 2000 rpm170 ppm, 6000 rpm170 ppm, 2000 rpm170 ppm,500 rpm blank, 2000 rpm

Figure A.6 Average corrosion rate of carbon steel in CO2 saturated NaCl solution: pH

5.5, 50oC, different HAc concentration and rotation speed.

160

161

162

163

164

165

166

167

168

169

170

171

LIST OF PUBLICATIONS

Journals

1. A Statistics Approach for the Prediction of CO2 Corrosion in Mixed Acid

Gases, Corrosion and materials, Australasian Corrosion Association, 2009.

2. Application of response surface methodology for Prediction CO2 Corrosion

Models at pH 4, International Journal of Corrosion, Hindawi, 2009 (minor

correction).

3. Optimization Design and Analytical Modeling in of CO2 corrosion

Experiments, International Journal of Corrosion , Hindawi, 2010 (in press).

4. Application of response surface methodology for Prediction CO2 Corrosion

Models at pH 5.5 (submitted to Engineering Journal, Taylor University, 2010)

Conferences

5. Mechanistic Prediction Model of CO2 Corrosion, International Graduated

Conference, UTM, Malaysia, 2008.

6. Study Corrosion Prediction Models in CO2 Environment, International

Conference, UTP, Malaysia, 2008

7. Modeling Simultaneous Effects of Pressure, Temperature and pH on CO2

Corrosion, Submitted to National Conference, UTP, Malaysia, 2009

8. Application of Response Surface Design to Characterize CO2 Corrosion

Mechanistically, Asia Pacific Nace Conference, 2009. (selected to published

in magazine of petromin/pipeline)

9. Study Combinations Effects of HAc in H2S/CO2 Corrosion, submit to ICPER,

UTP, 2010 (selected to publish in applied science journal)

10. Study on the Effect of Surface Finish on Corrosion of Carbon Steel in CO2

Environment, ICPER, 2010. (selected to publish in applied science journal)